id	sid	tid	token	lemma	pos
ajrhss-2192	1	1	american	american	PROPN
ajrhss-2192	1	2	journal	journal	PROPN
ajrhss-2192	1	3	of	of	ADP
ajrhss-2192	1	4	research	research	NOUN
ajrhss-2192	1	5	in	in	ADP
ajrhss-2192	1	6	humanities	humanity	NOUN
ajrhss-2192	1	7	and	and	CCONJ
ajrhss-2192	1	8	social	social	ADJ
ajrhss-2192	1	9	sciences	science	NOUN
ajrhss-2192	1	10	issn	issn	PROPN
ajrhss-2192	1	11	(	(	PUNCT
ajrhss-2192	1	12	e	e	NOUN
ajrhss-2192	1	13	):	):	PUNCT
ajrhss-2192	1	14	2832	2832	NUM
ajrhss-2192	1	15	-	-	SYM
ajrhss-2192	1	16	8019	8019	NUM
ajrhss-2192	1	17	volume	volume	NOUN
ajrhss-2192	1	18	25	25	NUM
ajrhss-2192	1	19	,	,	PUNCT
ajrhss-2192	1	20	|	|	ADV
ajrhss-2192	1	21	june	june	PROPN
ajrhss-2192	1	22	2024	2024	NUM
ajrhss-2192	1	23	p	p	NOUN
ajrhss-2192	1	24	a	a	DET
ajrhss-2192	1	25	g	g	NOUN
ajrhss-2192	1	26	e	e	NOUN
ajrhss-2192	1	27	|	|	ADV
ajrhss-2192	1	28	30	30	NUM
ajrhss-2192	1	29	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	1	30	exponential	exponential	ADJ
ajrhss-2192	1	31	function	function	NOUN
ajrhss-2192	1	32	abdurashitov	abdurashitov	PROPN
ajrhss-2192	1	33	rakhmatullo	rakhmatullo	PROPN
ajrhss-2192	1	34	abdukhamitovich	abdukhamitovich	PROPN
ajrhss-2192	1	35	khusenov	khusenov	PROPN
ajrhss-2192	1	36	zikrillo	zikrillo	PROPN
ajrhss-2192	1	37	raxmatillo	raxmatillo	VERB
ajrhss-2192	1	38	ogli	ogli	NOUN
ajrhss-2192	2	1	adkhamov	adkhamov	PROPN
ajrhss-2192	2	2	khasanboy	khasanboy	PROPN
ajrhss-2192	2	3	abdusalom	abdusalom	PROPN
ajrhss-2192	2	4	ogli	ogli	PROPN
ajrhss-2192	2	5	a	a	DET
ajrhss-2192	2	6	b	b	PROPN
ajrhss-2192	2	7	s	s	ADP
ajrhss-2192	2	8	t	t	PROPN
ajrhss-2192	2	9	r	r	NOUN
ajrhss-2192	2	10	a	a	DET
ajrhss-2192	2	11	c	c	NOUN
ajrhss-2192	2	12	t	t	NOUN
ajrhss-2192	2	13	k	k	X
ajrhss-2192	2	14	e	e	PROPN
ajrhss-2192	2	15	y	y	PROPN
ajrhss-2192	2	16	w	w	NOUN
ajrhss-2192	3	1	o	o	NOUN
ajrhss-2192	3	2	r	r	NOUN
ajrhss-2192	3	3	d	d	PROPN
ajrhss-2192	3	4	s	s	VERB
ajrhss-2192	3	5	this	this	DET
ajrhss-2192	3	6	article	article	NOUN
ajrhss-2192	3	7	provides	provide	VERB
ajrhss-2192	3	8	information	information	NOUN
ajrhss-2192	3	9	about	about	ADP
ajrhss-2192	3	10	the	the	DET
ajrhss-2192	3	11	exponential	exponential	ADJ
ajrhss-2192	3	12	function	function	NOUN
ajrhss-2192	3	13	and	and	CCONJ
ajrhss-2192	3	14	its	its	PRON
ajrhss-2192	3	15	role	role	NOUN
ajrhss-2192	3	16	in	in	ADP
ajrhss-2192	3	17	mathematics	mathematic	NOUN
ajrhss-2192	3	18	.	.	PUNCT
ajrhss-2192	4	1	exponential	exponential	ADJ
ajrhss-2192	4	2	function	function	NOUN
ajrhss-2192	4	3	,	,	PUNCT
ajrhss-2192	4	4	growth	growth	NOUN
ajrhss-2192	4	5	and	and	CCONJ
ajrhss-2192	4	6	decay	decay	NOUN
ajrhss-2192	4	7	,	,	PUNCT
ajrhss-2192	4	8	natural	natural	ADJ
ajrhss-2192	4	9	exponential	exponential	ADJ
ajrhss-2192	4	10	function	function	NOUN
ajrhss-2192	4	11	,	,	PUNCT
ajrhss-2192	4	12	base	base	NOUN
ajrhss-2192	4	13	,	,	PUNCT
ajrhss-2192	4	14	initial	initial	ADJ
ajrhss-2192	4	15	value	value	NOUN
ajrhss-2192	4	16	,	,	PUNCT
ajrhss-2192	4	17	differential	differential	ADJ
ajrhss-2192	4	18	equations	equation	NOUN
ajrhss-2192	4	19	,	,	PUNCT
ajrhss-2192	4	20	compound	compound	NOUN
ajrhss-2192	4	21	interest	interest	NOUN
ajrhss-2192	4	22	,	,	PUNCT
ajrhss-2192	4	23	radioactive	radioactive	ADJ
ajrhss-2192	4	24	decay	decay	NOUN
ajrhss-2192	4	25	,	,	PUNCT
ajrhss-2192	4	26	logarithm	logarithm	PROPN
ajrhss-2192	4	27	,	,	PUNCT
ajrhss-2192	4	28	taylor	taylor	PROPN
ajrhss-2192	4	29	series	series	PROPN
ajrhss-2192	4	30	,	,	PUNCT
ajrhss-2192	4	31	complex	complex	ADJ
ajrhss-2192	4	32	analysis	analysis	NOUN
ajrhss-2192	4	33	introduction	introduction	NOUN
ajrhss-2192	4	34	an	an	DET
ajrhss-2192	4	35	exponential	exponential	ADJ
ajrhss-2192	4	36	function	function	NOUN
ajrhss-2192	4	37	is	be	AUX
ajrhss-2192	4	38	a	a	DET
ajrhss-2192	4	39	mathematical	mathematical	ADJ
ajrhss-2192	4	40	function	function	NOUN
ajrhss-2192	4	41	of	of	ADP
ajrhss-2192	4	42	the	the	DET
ajrhss-2192	4	43	form	form	NOUN
ajrhss-2192	4	44	\	\	PROPN
ajrhss-2192	4	45	(	(	PUNCT
ajrhss-2192	4	46	f(x	f(x	PROPN
ajrhss-2192	4	47	)	)	PUNCT
ajrhss-2192	4	48	=	=	PUNCT
ajrhss-2192	4	49	a	a	DET
ajrhss-2192	4	50	\cdot	\cdot	NOUN
ajrhss-2192	4	51	b^x	b^x	PROPN
ajrhss-2192	4	52	\	\	PROPN
ajrhss-2192	4	53	)	)	PUNCT
ajrhss-2192	4	54	,	,	PUNCT
ajrhss-2192	4	55	where	where	SCONJ
ajrhss-2192	4	56	:	:	PUNCT
ajrhss-2192	4	57	\	\	PROPN
ajrhss-2192	4	58	(	(	PUNCT
ajrhss-2192	4	59	a	a	DET
ajrhss-2192	4	60	\	\	NOUN
ajrhss-2192	4	61	)	)	PUNCT
ajrhss-2192	4	62	is	be	AUX
ajrhss-2192	4	63	a	a	DET
ajrhss-2192	4	64	constant	constant	ADJ
ajrhss-2192	4	65	that	that	PRON
ajrhss-2192	4	66	represents	represent	VERB
ajrhss-2192	4	67	the	the	DET
ajrhss-2192	4	68	initial	initial	ADJ
ajrhss-2192	4	69	value	value	NOUN
ajrhss-2192	4	70	or	or	CCONJ
ajrhss-2192	4	71	the	the	DET
ajrhss-2192	4	72	y	y	NOUN
ajrhss-2192	4	73	-	-	PUNCT
ajrhss-2192	4	74	intercept	intercept	NOUN
ajrhss-2192	4	75	of	of	ADP
ajrhss-2192	4	76	the	the	DET
ajrhss-2192	4	77	function	function	NOUN
ajrhss-2192	4	78	.	.	PUNCT
ajrhss-2192	5	1	\	\	PROPN
ajrhss-2192	5	2	(	(	PUNCT
ajrhss-2192	5	3	b	b	X
ajrhss-2192	5	4	\	\	NOUN
ajrhss-2192	5	5	)	)	PUNCT
ajrhss-2192	5	6	is	be	AUX
ajrhss-2192	5	7	the	the	DET
ajrhss-2192	5	8	base	base	NOUN
ajrhss-2192	5	9	of	of	ADP
ajrhss-2192	5	10	the	the	DET
ajrhss-2192	5	11	exponential	exponential	ADJ
ajrhss-2192	5	12	function	function	NOUN
ajrhss-2192	5	13	,	,	PUNCT
ajrhss-2192	5	14	which	which	PRON
ajrhss-2192	5	15	is	be	AUX
ajrhss-2192	5	16	a	a	DET
ajrhss-2192	5	17	positive	positive	ADJ
ajrhss-2192	5	18	real	real	ADJ
ajrhss-2192	5	19	number	number	NOUN
ajrhss-2192	5	20	.	.	PUNCT
ajrhss-2192	6	1	\	\	PROPN
ajrhss-2192	6	2	(	(	PUNCT
ajrhss-2192	6	3	x	x	SYM
ajrhss-2192	6	4	\	\	PROPN
ajrhss-2192	6	5	)	)	PUNCT
ajrhss-2192	6	6	is	be	AUX
ajrhss-2192	6	7	the	the	DET
ajrhss-2192	6	8	exponent	exponent	NOUN
ajrhss-2192	6	9	,	,	PUNCT
ajrhss-2192	6	10	which	which	PRON
ajrhss-2192	6	11	can	can	AUX
ajrhss-2192	6	12	be	be	AUX
ajrhss-2192	6	13	any	any	DET
ajrhss-2192	6	14	real	real	ADJ
ajrhss-2192	6	15	number	number	NOUN
ajrhss-2192	6	16	.	.	PUNCT
ajrhss-2192	7	1	the	the	DET
ajrhss-2192	7	2	most	most	ADV
ajrhss-2192	7	3	common	common	ADJ
ajrhss-2192	7	4	base	base	NOUN
ajrhss-2192	7	5	for	for	ADP
ajrhss-2192	7	6	exponential	exponential	ADJ
ajrhss-2192	7	7	functions	function	NOUN
ajrhss-2192	7	8	in	in	ADP
ajrhss-2192	7	9	mathematics	mathematic	NOUN
ajrhss-2192	7	10	is	be	AUX
ajrhss-2192	7	11	\	\	PROPN
ajrhss-2192	7	12	(	(	PUNCT
ajrhss-2192	7	13	e	e	NOUN
ajrhss-2192	7	14	\	\	PROPN
ajrhss-2192	7	15	)	)	PUNCT
ajrhss-2192	7	16	(	(	PUNCT
ajrhss-2192	7	17	approximately	approximately	ADV
ajrhss-2192	7	18	2.71828	2.71828	NUM
ajrhss-2192	7	19	)	)	PUNCT
ajrhss-2192	7	20	,	,	PUNCT
ajrhss-2192	7	21	leading	lead	VERB
ajrhss-2192	7	22	to	to	ADP
ajrhss-2192	7	23	the	the	DET
ajrhss-2192	7	24	natural	natural	ADJ
ajrhss-2192	7	25	exponential	exponential	ADJ
ajrhss-2192	7	26	function	function	NOUN
ajrhss-2192	7	27	\	\	PROPN
ajrhss-2192	7	28	(	(	PUNCT
ajrhss-2192	7	29	f(x	f(x	PROPN
ajrhss-2192	7	30	)	)	PUNCT
ajrhss-2192	8	1	=	=	PUNCT
ajrhss-2192	8	2	e^x	e^x	NOUN
ajrhss-2192	8	3	\	\	PROPN
ajrhss-2192	8	4	)	)	PUNCT
ajrhss-2192	8	5	.	.	PUNCT
ajrhss-2192	9	1	exponential	exponential	ADJ
ajrhss-2192	9	2	functions	function	NOUN
ajrhss-2192	9	3	are	be	AUX
ajrhss-2192	9	4	characterized	characterize	VERB
ajrhss-2192	9	5	by	by	ADP
ajrhss-2192	9	6	their	their	PRON
ajrhss-2192	9	7	rapid	rapid	ADJ
ajrhss-2192	9	8	growth	growth	NOUN
ajrhss-2192	9	9	or	or	CCONJ
ajrhss-2192	9	10	decay	decay	NOUN
ajrhss-2192	9	11	.	.	PUNCT
ajrhss-2192	10	1	when	when	SCONJ
ajrhss-2192	10	2	\	\	PROPN
ajrhss-2192	10	3	(	(	PUNCT
ajrhss-2192	10	4	b	b	X
ajrhss-2192	10	5	>	>	SYM
ajrhss-2192	10	6	1	1	NUM
ajrhss-2192	10	7	\	\	NOUN
ajrhss-2192	10	8	)	)	PUNCT
ajrhss-2192	10	9	,	,	PUNCT
ajrhss-2192	10	10	the	the	DET
ajrhss-2192	10	11	function	function	NOUN
ajrhss-2192	10	12	describes	describe	VERB
ajrhss-2192	10	13	exponential	exponential	ADJ
ajrhss-2192	10	14	growth	growth	NOUN
ajrhss-2192	10	15	,	,	PUNCT
ajrhss-2192	10	16	and	and	CCONJ
ajrhss-2192	10	17	when	when	SCONJ
ajrhss-2192	10	18	\	\	PROPN
ajrhss-2192	10	19	(	(	PUNCT
ajrhss-2192	10	20	0	0	NUM
ajrhss-2192	10	21	<	<	X
ajrhss-2192	10	22	b	b	X
ajrhss-2192	10	23	<	<	X
ajrhss-2192	10	24	1	1	NUM
ajrhss-2192	10	25	\	\	NOUN
ajrhss-2192	10	26	)	)	PUNCT
ajrhss-2192	10	27	,	,	PUNCT
ajrhss-2192	10	28	it	it	PRON
ajrhss-2192	10	29	describes	describe	VERB
ajrhss-2192	10	30	exponential	exponential	ADJ
ajrhss-2192	10	31	decay	decay	NOUN
ajrhss-2192	10	32	.	.	PUNCT
ajrhss-2192	11	1	exponential	exponential	ADJ
ajrhss-2192	11	2	functions	function	NOUN
ajrhss-2192	11	3	have	have	VERB
ajrhss-2192	11	4	several	several	ADJ
ajrhss-2192	11	5	important	important	ADJ
ajrhss-2192	11	6	properties	property	NOUN
ajrhss-2192	11	7	:	:	PUNCT
ajrhss-2192	11	8	the	the	DET
ajrhss-2192	11	9	function	function	NOUN
ajrhss-2192	11	10	is	be	AUX
ajrhss-2192	11	11	always	always	ADV
ajrhss-2192	11	12	positive	positive	ADJ
ajrhss-2192	11	13	for	for	ADP
ajrhss-2192	11	14	all	all	DET
ajrhss-2192	11	15	real	real	ADJ
ajrhss-2192	11	16	values	value	NOUN
ajrhss-2192	11	17	of	of	ADP
ajrhss-2192	11	18	\	\	PROPN
ajrhss-2192	11	19	(	(	PUNCT
ajrhss-2192	11	20	x	x	SYM
ajrhss-2192	11	21	\	\	PROPN
ajrhss-2192	11	22	)	)	PUNCT
ajrhss-2192	11	23	.	.	PUNCT
ajrhss-2192	12	1	the	the	DET
ajrhss-2192	12	2	rate	rate	NOUN
ajrhss-2192	12	3	of	of	ADP
ajrhss-2192	12	4	growth	growth	NOUN
ajrhss-2192	12	5	(	(	PUNCT
ajrhss-2192	12	6	or	or	CCONJ
ajrhss-2192	12	7	decay	decay	NOUN
ajrhss-2192	12	8	)	)	PUNCT
ajrhss-2192	12	9	of	of	ADP
ajrhss-2192	12	10	the	the	DET
ajrhss-2192	12	11	function	function	NOUN
ajrhss-2192	12	12	is	be	AUX
ajrhss-2192	12	13	proportional	proportional	ADJ
ajrhss-2192	12	14	to	to	ADP
ajrhss-2192	12	15	its	its	PRON
ajrhss-2192	12	16	current	current	ADJ
ajrhss-2192	12	17	value	value	NOUN
ajrhss-2192	12	18	.	.	PUNCT
ajrhss-2192	13	1	the	the	DET
ajrhss-2192	13	2	graph	graph	NOUN
ajrhss-2192	13	3	of	of	ADP
ajrhss-2192	13	4	an	an	DET
ajrhss-2192	13	5	exponential	exponential	ADJ
ajrhss-2192	13	6	function	function	NOUN
ajrhss-2192	13	7	is	be	AUX
ajrhss-2192	13	8	a	a	DET
ajrhss-2192	13	9	smooth	smooth	ADJ
ajrhss-2192	13	10	curve	curve	NOUN
ajrhss-2192	13	11	that	that	SCONJ
ajrhss-2192	13	12	either	either	CCONJ
ajrhss-2192	13	13	increases	increase	NOUN
ajrhss-2192	13	14	(	(	PUNCT
ajrhss-2192	13	15	for	for	ADP
ajrhss-2192	13	16	growth	growth	NOUN
ajrhss-2192	13	17	)	)	PUNCT
ajrhss-2192	13	18	or	or	CCONJ
ajrhss-2192	13	19	decreases	decrease	NOUN
ajrhss-2192	13	20	(	(	PUNCT
ajrhss-2192	13	21	for	for	ADP
ajrhss-2192	13	22	decay	decay	NOUN
ajrhss-2192	13	23	)	)	PUNCT
ajrhss-2192	13	24	exponentially	exponentially	ADV
ajrhss-2192	13	25	.	.	PUNCT
ajrhss-2192	14	1	exponential	exponential	ADJ
ajrhss-2192	14	2	functions	function	NOUN
ajrhss-2192	14	3	are	be	AUX
ajrhss-2192	14	4	widely	widely	ADV
ajrhss-2192	14	5	used	use	VERB
ajrhss-2192	14	6	in	in	ADP
ajrhss-2192	14	7	various	various	ADJ
ajrhss-2192	14	8	fields	field	NOUN
ajrhss-2192	14	9	,	,	PUNCT
ajrhss-2192	14	10	including	include	VERB
ajrhss-2192	14	11	biology	biology	NOUN
ajrhss-2192	14	12	(	(	PUNCT
ajrhss-2192	14	13	population	population	NOUN
ajrhss-2192	14	14	growth	growth	NOUN
ajrhss-2192	14	15	)	)	PUNCT
ajrhss-2192	14	16	,	,	PUNCT
ajrhss-2192	14	17	finance	finance	NOUN
ajrhss-2192	14	18	(	(	PUNCT
ajrhss-2192	14	19	compound	compound	NOUN
ajrhss-2192	14	20	interest	interest	NOUN
ajrhss-2192	14	21	)	)	PUNCT
ajrhss-2192	14	22	,	,	PUNCT
ajrhss-2192	14	23	physics	physics	NOUN
ajrhss-2192	14	24	(	(	PUNCT
ajrhss-2192	14	25	radioactive	radioactive	ADJ
ajrhss-2192	14	26	decay	decay	NOUN
ajrhss-2192	14	27	)	)	PUNCT
ajrhss-2192	14	28	,	,	PUNCT
ajrhss-2192	14	29	and	and	CCONJ
ajrhss-2192	14	30	many	many	ADJ
ajrhss-2192	14	31	other	other	ADJ
ajrhss-2192	14	32	areas	area	NOUN
ajrhss-2192	14	33	where	where	SCONJ
ajrhss-2192	14	34	processes	process	VERB
ajrhss-2192	14	35	change	change	VERB
ajrhss-2192	14	36	rapidly	rapidly	ADV
ajrhss-2192	14	37	relative	relative	ADJ
ajrhss-2192	14	38	to	to	ADP
ajrhss-2192	14	39	their	their	PRON
ajrhss-2192	14	40	size	size	NOUN
ajrhss-2192	14	41	.	.	PUNCT
ajrhss-2192	15	1	here	here	ADV
ajrhss-2192	15	2	's	be	AUX
ajrhss-2192	15	3	a	a	DET
ajrhss-2192	15	4	more	more	ADV
ajrhss-2192	15	5	detailed	detailed	ADJ
ajrhss-2192	15	6	look	look	NOUN
ajrhss-2192	15	7	at	at	ADP
ajrhss-2192	15	8	exponential	exponential	ADJ
ajrhss-2192	15	9	functions	function	NOUN
ajrhss-2192	15	10	,	,	PUNCT
ajrhss-2192	15	11	including	include	VERB
ajrhss-2192	15	12	their	their	PRON
ajrhss-2192	15	13	properties	property	NOUN
ajrhss-2192	15	14	,	,	PUNCT
ajrhss-2192	15	15	applications	application	NOUN
ajrhss-2192	15	16	,	,	PUNCT
ajrhss-2192	15	17	and	and	CCONJ
ajrhss-2192	15	18	key	key	ADJ
ajrhss-2192	15	19	concepts	concept	NOUN
ajrhss-2192	15	20	:	:	PUNCT
ajrhss-2192	15	21	definition	definition	NOUN
ajrhss-2192	15	22	and	and	CCONJ
ajrhss-2192	15	23	basic	basic	ADJ
ajrhss-2192	15	24	form	form	NOUN
ajrhss-2192	15	25	an	an	DET
ajrhss-2192	15	26	exponential	exponential	ADJ
ajrhss-2192	15	27	function	function	NOUN
ajrhss-2192	15	28	can	can	AUX
ajrhss-2192	15	29	be	be	AUX
ajrhss-2192	15	30	written	write	VERB
ajrhss-2192	15	31	as	as	ADP
ajrhss-2192	15	32	:	:	PUNCT
ajrhss-2192	15	33	\	\	PROPN
ajrhss-2192	15	34	[	[	PUNCT
ajrhss-2192	15	35	f(x	f(x	PROPN
ajrhss-2192	15	36	)	)	PUNCT
ajrhss-2192	15	37	=	=	PUNCT
ajrhss-2192	16	1	a	a	DET
ajrhss-2192	16	2	\cdot	\cdot	NOUN
ajrhss-2192	16	3	b^x	b^x	NOUN
ajrhss-2192	16	4	\	\	PROPN
ajrhss-2192	16	5	]	]	PUNCT
ajrhss-2192	16	6	where	where	SCONJ
ajrhss-2192	16	7	:	:	PUNCT
ajrhss-2192	16	8	american	american	ADJ
ajrhss-2192	16	9	journal	journal	PROPN
ajrhss-2192	16	10	of	of	ADP
ajrhss-2192	16	11	research	research	NOUN
ajrhss-2192	16	12	in	in	ADP
ajrhss-2192	16	13	humanities	humanity	NOUN
ajrhss-2192	16	14	and	and	CCONJ
ajrhss-2192	16	15	social	social	ADJ
ajrhss-2192	16	16	sciences	science	NOUN
ajrhss-2192	16	17	volume	volume	NOUN
ajrhss-2192	16	18	25	25	NUM
ajrhss-2192	16	19	june	june	PROPN
ajrhss-2192	16	20	2024	2024	NUM
ajrhss-2192	16	21	p	p	NOUN
ajrhss-2192	16	22	a	a	DET
ajrhss-2192	16	23	g	g	NOUN
ajrhss-2192	16	24	e	e	NOUN
ajrhss-2192	16	25	|	|	ADV
ajrhss-2192	16	26	31	31	NUM
ajrhss-2192	16	27	www.americanjournal.org	www.americanjournal.org	PROPN
ajrhss-2192	16	28	\	\	PROPN
ajrhss-2192	16	29	(	(	PUNCT
ajrhss-2192	16	30	a	a	DET
ajrhss-2192	16	31	\	\	PROPN
ajrhss-2192	16	32	)	)	PUNCT
ajrhss-2192	16	33	(	(	PUNCT
ajrhss-2192	16	34	initial	initial	ADJ
ajrhss-2192	16	35	value	value	NOUN
ajrhss-2192	16	36	):	):	PUNCT
ajrhss-2192	16	37	determines	determine	VERB
ajrhss-2192	16	38	the	the	DET
ajrhss-2192	16	39	vertical	vertical	ADJ
ajrhss-2192	16	40	stretch	stretch	NOUN
ajrhss-2192	16	41	or	or	CCONJ
ajrhss-2192	16	42	compression	compression	NOUN
ajrhss-2192	16	43	and	and	CCONJ
ajrhss-2192	16	44	the	the	DET
ajrhss-2192	16	45	direction	direction	NOUN
ajrhss-2192	16	46	(	(	PUNCT
ajrhss-2192	16	47	upwards	upwards	ADV
ajrhss-2192	16	48	for	for	ADP
ajrhss-2192	16	49	positive	positive	ADJ
ajrhss-2192	16	50	\	\	NOUN
ajrhss-2192	16	51	(	(	PUNCT
ajrhss-2192	16	52	a	a	DET
ajrhss-2192	16	53	\	\	NOUN
ajrhss-2192	16	54	)	)	PUNCT
ajrhss-2192	16	55	and	and	CCONJ
ajrhss-2192	16	56	downwards	downward	NOUN
ajrhss-2192	16	57	for	for	ADP
ajrhss-2192	16	58	negative	negative	ADJ
ajrhss-2192	16	59	\	\	NOUN
ajrhss-2192	16	60	(	(	PUNCT
ajrhss-2192	16	61	a	a	DET
ajrhss-2192	16	62	\	\	NOUN
ajrhss-2192	16	63	)	)	PUNCT
ajrhss-2192	16	64	)	)	PUNCT
ajrhss-2192	16	65	.	.	PUNCT
ajrhss-2192	17	1	\	\	PROPN
ajrhss-2192	17	2	(	(	PUNCT
ajrhss-2192	17	3	b	b	PROPN
ajrhss-2192	17	4	\	\	PROPN
ajrhss-2192	17	5	)	)	PUNCT
ajrhss-2192	17	6	(	(	PUNCT
ajrhss-2192	17	7	base	base	NOUN
ajrhss-2192	17	8	):	):	PUNCT
ajrhss-2192	17	9	determines	determine	VERB
ajrhss-2192	17	10	the	the	DET
ajrhss-2192	17	11	rate	rate	NOUN
ajrhss-2192	17	12	of	of	ADP
ajrhss-2192	17	13	growth	growth	NOUN
ajrhss-2192	17	14	(	(	PUNCT
ajrhss-2192	17	15	if	if	SCONJ
ajrhss-2192	17	16	\	\	PROPN
ajrhss-2192	17	17	(	(	PUNCT
ajrhss-2192	17	18	b	b	X
ajrhss-2192	17	19	>	>	SYM
ajrhss-2192	17	20	1	1	NUM
ajrhss-2192	17	21	\	\	NOUN
ajrhss-2192	17	22	)	)	PUNCT
ajrhss-2192	17	23	)	)	PUNCT
ajrhss-2192	17	24	or	or	CCONJ
ajrhss-2192	17	25	decay	decay	NOUN
ajrhss-2192	17	26	(	(	PUNCT
ajrhss-2192	17	27	if	if	SCONJ
ajrhss-2192	17	28	\	\	PROPN
ajrhss-2192	17	29	(	(	PUNCT
ajrhss-2192	17	30	0	0	NUM
ajrhss-2192	17	31	<	<	X
ajrhss-2192	17	32	b	b	X
ajrhss-2192	17	33	<	<	X
ajrhss-2192	17	34	1	1	NUM
ajrhss-2192	17	35	\	\	NOUN
ajrhss-2192	17	36	)	)	PUNCT
ajrhss-2192	17	37	)	)	PUNCT
ajrhss-2192	17	38	.	.	PUNCT
ajrhss-2192	18	1	\	\	PROPN
ajrhss-2192	18	2	(	(	PUNCT
ajrhss-2192	18	3	x	x	SYM
ajrhss-2192	18	4	\	\	PROPN
ajrhss-2192	18	5	):	):	PUNCT
ajrhss-2192	18	6	the	the	DET
ajrhss-2192	18	7	exponent	exponent	NOUN
ajrhss-2192	18	8	,	,	PUNCT
ajrhss-2192	18	9	which	which	PRON
ajrhss-2192	18	10	is	be	AUX
ajrhss-2192	18	11	the	the	DET
ajrhss-2192	18	12	variable	variable	NOUN
ajrhss-2192	18	13	.	.	PUNCT
ajrhss-2192	19	1	key	key	ADJ
ajrhss-2192	19	2	properties	property	NOUN
ajrhss-2192	19	3	1	1	NUM
ajrhss-2192	19	4	.	.	PUNCT
ajrhss-2192	19	5	growth	growth	NOUN
ajrhss-2192	19	6	and	and	CCONJ
ajrhss-2192	19	7	decay	decay	NOUN
ajrhss-2192	19	8	:	:	PUNCT
ajrhss-2192	19	9	if	if	SCONJ
ajrhss-2192	19	10	\	\	PROPN
ajrhss-2192	19	11	(	(	PUNCT
ajrhss-2192	19	12	b	b	X
ajrhss-2192	19	13	>	>	SYM
ajrhss-2192	19	14	1	1	NUM
ajrhss-2192	19	15	\	\	NOUN
ajrhss-2192	19	16	)	)	PUNCT
ajrhss-2192	19	17	,	,	PUNCT
ajrhss-2192	19	18	the	the	DET
ajrhss-2192	19	19	function	function	NOUN
ajrhss-2192	19	20	represents	represent	VERB
ajrhss-2192	19	21	exponential	exponential	ADJ
ajrhss-2192	19	22	growth	growth	NOUN
ajrhss-2192	19	23	.	.	PUNCT
ajrhss-2192	20	1	if	if	SCONJ
ajrhss-2192	20	2	\	\	PROPN
ajrhss-2192	20	3	(	(	PUNCT
ajrhss-2192	20	4	0	0	NUM
ajrhss-2192	20	5	<	<	X
ajrhss-2192	20	6	b	b	X
ajrhss-2192	20	7	<	<	X
ajrhss-2192	20	8	1	1	NUM
ajrhss-2192	20	9	\	\	NOUN
ajrhss-2192	20	10	)	)	PUNCT
ajrhss-2192	20	11	,	,	PUNCT
ajrhss-2192	20	12	the	the	DET
ajrhss-2192	20	13	function	function	NOUN
ajrhss-2192	20	14	represents	represent	VERB
ajrhss-2192	20	15	exponential	exponential	ADJ
ajrhss-2192	20	16	decay	decay	NOUN
ajrhss-2192	20	17	.	.	PUNCT
ajrhss-2192	21	1	2	2	X
ajrhss-2192	21	2	.	.	X
ajrhss-2192	21	3	horizontal	horizontal	ADJ
ajrhss-2192	21	4	asymptote	asymptote	NOUN
ajrhss-2192	21	5	:	:	PUNCT
ajrhss-2192	21	6	the	the	DET
ajrhss-2192	21	7	x	x	NOUN
ajrhss-2192	21	8	-	-	NOUN
ajrhss-2192	21	9	axis	axis	ADJ
ajrhss-2192	21	10	(	(	PUNCT
ajrhss-2192	21	11	y	y	NOUN
ajrhss-2192	21	12	=	=	SYM
ajrhss-2192	21	13	0	0	NUM
ajrhss-2192	21	14	)	)	PUNCT
ajrhss-2192	21	15	is	be	AUX
ajrhss-2192	21	16	a	a	DET
ajrhss-2192	21	17	horizontal	horizontal	ADJ
ajrhss-2192	21	18	asymptote	asymptote	NOUN
ajrhss-2192	21	19	of	of	ADP
ajrhss-2192	21	20	the	the	DET
ajrhss-2192	21	21	function	function	NOUN
ajrhss-2192	21	22	.	.	PUNCT
ajrhss-2192	22	1	as	as	SCONJ
ajrhss-2192	22	2	\	\	PROPN
ajrhss-2192	22	3	(	(	PUNCT
ajrhss-2192	22	4	x	x	SYM
ajrhss-2192	22	5	\	\	ADJ
ajrhss-2192	22	6	)	)	PUNCT
ajrhss-2192	22	7	approaches	approach	VERB
ajrhss-2192	22	8	negative	negative	ADJ
ajrhss-2192	22	9	infinity	infinity	NOUN
ajrhss-2192	22	10	,	,	PUNCT
ajrhss-2192	22	11	\	\	PROPN
ajrhss-2192	22	12	(	(	PUNCT
ajrhss-2192	22	13	f(x	f(x	PROPN
ajrhss-2192	22	14	)	)	PUNCT
ajrhss-2192	23	1	\	\	NOUN
ajrhss-2192	23	2	)	)	PUNCT
ajrhss-2192	23	3	approaches	approach	VERB
ajrhss-2192	23	4	0	0	PUNCT
ajrhss-2192	24	1	but	but	CCONJ
ajrhss-2192	24	2	never	never	ADV
ajrhss-2192	24	3	actually	actually	ADV
ajrhss-2192	24	4	reaches	reach	VERB
ajrhss-2192	24	5	it	it	PRON
ajrhss-2192	24	6	.	.	PUNCT
ajrhss-2192	25	1	3	3	X
ajrhss-2192	25	2	.	.	X
ajrhss-2192	25	3	y	y	X
ajrhss-2192	25	4	-	-	PUNCT
ajrhss-2192	25	5	intercept	intercept	NOUN
ajrhss-2192	25	6	:	:	PUNCT
ajrhss-2192	25	7	when	when	SCONJ
ajrhss-2192	25	8	\	\	PROPN
ajrhss-2192	25	9	(	(	PUNCT
ajrhss-2192	25	10	x	x	SYM
ajrhss-2192	25	11	=	=	SYM
ajrhss-2192	25	12	0	0	NUM
ajrhss-2192	25	13	\	\	NOUN
ajrhss-2192	25	14	)	)	PUNCT
ajrhss-2192	25	15	,	,	PUNCT
ajrhss-2192	25	16	\	\	PROPN
ajrhss-2192	25	17	(	(	PUNCT
ajrhss-2192	25	18	f(0	f(0	NOUN
ajrhss-2192	25	19	)	)	PUNCT
ajrhss-2192	25	20	=	=	PUNCT
ajrhss-2192	25	21	a	a	DET
ajrhss-2192	25	22	\cdot	\cdot	NOUN
ajrhss-2192	25	23	b^0	b^0	NOUN
ajrhss-2192	25	24	=	=	PUNCT
ajrhss-2192	25	25	a	a	DET
ajrhss-2192	25	26	\cdot	\cdot	NOUN
ajrhss-2192	25	27	1	1	NUM
ajrhss-2192	25	28	=	=	PUNCT
ajrhss-2192	25	29	a	a	DET
ajrhss-2192	25	30	\	\	NOUN
ajrhss-2192	25	31	)	)	PUNCT
ajrhss-2192	25	32	.	.	PUNCT
ajrhss-2192	26	1	thus	thus	ADV
ajrhss-2192	26	2	,	,	PUNCT
ajrhss-2192	26	3	the	the	DET
ajrhss-2192	26	4	y	y	NOUN
ajrhss-2192	26	5	-	-	PUNCT
ajrhss-2192	26	6	intercept	intercept	NOUN
ajrhss-2192	26	7	is	be	AUX
ajrhss-2192	26	8	at	at	ADP
ajrhss-2192	26	9	\	\	PROPN
ajrhss-2192	26	10	(	(	PUNCT
ajrhss-2192	26	11	(	(	PUNCT
ajrhss-2192	26	12	0	0	NUM
ajrhss-2192	26	13	,	,	PUNCT
ajrhss-2192	26	14	a	a	PRON
ajrhss-2192	26	15	)	)	PUNCT
ajrhss-2192	26	16	\	\	NOUN
ajrhss-2192	26	17	)	)	PUNCT
ajrhss-2192	26	18	.	.	PUNCT
ajrhss-2192	27	1	4	4	X
ajrhss-2192	27	2	.	.	X
ajrhss-2192	27	3	domain	domain	NOUN
ajrhss-2192	27	4	and	and	CCONJ
ajrhss-2192	27	5	range	range	NOUN
ajrhss-2192	27	6	:	:	PUNCT
ajrhss-2192	27	7	the	the	DET
ajrhss-2192	27	8	domain	domain	NOUN
ajrhss-2192	27	9	of	of	ADP
ajrhss-2192	27	10	an	an	DET
ajrhss-2192	27	11	exponential	exponential	ADJ
ajrhss-2192	27	12	function	function	NOUN
ajrhss-2192	27	13	is	be	AUX
ajrhss-2192	27	14	all	all	DET
ajrhss-2192	27	15	real	real	ADJ
ajrhss-2192	27	16	numbers	number	NOUN
ajrhss-2192	27	17	(	(	PUNCT
ajrhss-2192	27	18	\	\	PROPN
ajrhss-2192	27	19	(	(	PUNCT
ajrhss-2192	27	20	-\infty	-\infty	INTJ
ajrhss-2192	27	21	<	<	X
ajrhss-2192	27	22	x	x	X
ajrhss-2192	27	23	<	<	X
ajrhss-2192	27	24	\infty	\infty	PROPN
ajrhss-2192	27	25	\	\	PROPN
ajrhss-2192	27	26	)	)	PUNCT
ajrhss-2192	27	27	)	)	PUNCT
ajrhss-2192	27	28	.	.	PUNCT
ajrhss-2192	28	1	the	the	DET
ajrhss-2192	28	2	range	range	NOUN
ajrhss-2192	28	3	is	be	AUX
ajrhss-2192	28	4	all	all	PRON
ajrhss-2192	28	5	positive	positive	ADJ
ajrhss-2192	28	6	real	real	ADJ
ajrhss-2192	28	7	numbers	number	NOUN
ajrhss-2192	28	8	(	(	PUNCT
ajrhss-2192	28	9	\	\	PROPN
ajrhss-2192	28	10	(	(	PUNCT
ajrhss-2192	28	11	0	0	NUM
ajrhss-2192	28	12	<	<	X
ajrhss-2192	28	13	f(x	f(x	PROPN
ajrhss-2192	28	14	)	)	PUNCT
ajrhss-2192	28	15	<	<	X
ajrhss-2192	28	16	\infty	\infty	PROPN
ajrhss-2192	28	17	\	\	PROPN
ajrhss-2192	28	18	)	)	PUNCT
ajrhss-2192	28	19	)	)	PUNCT
ajrhss-2192	28	20	.	.	PUNCT
ajrhss-2192	29	1	graph	graph	NOUN
ajrhss-2192	29	2	characteristics	characteristic	NOUN
ajrhss-2192	29	3	the	the	DET
ajrhss-2192	29	4	graph	graph	NOUN
ajrhss-2192	29	5	is	be	AUX
ajrhss-2192	29	6	always	always	ADV
ajrhss-2192	29	7	increasing	increase	VERB
ajrhss-2192	29	8	(	(	PUNCT
ajrhss-2192	29	9	for	for	ADP
ajrhss-2192	29	10	\	\	PROPN
ajrhss-2192	29	11	(	(	PUNCT
ajrhss-2192	29	12	b	b	X
ajrhss-2192	29	13	>	>	SYM
ajrhss-2192	29	14	1	1	NUM
ajrhss-2192	29	15	\	\	NOUN
ajrhss-2192	29	16	)	)	PUNCT
ajrhss-2192	29	17	)	)	PUNCT
ajrhss-2192	29	18	or	or	CCONJ
ajrhss-2192	29	19	decreasing	decrease	VERB
ajrhss-2192	29	20	(	(	PUNCT
ajrhss-2192	29	21	for	for	ADP
ajrhss-2192	29	22	\	\	NOUN
ajrhss-2192	29	23	(	(	PUNCT
ajrhss-2192	29	24	0	0	NUM
ajrhss-2192	29	25	<	<	X
ajrhss-2192	29	26	b	b	X
ajrhss-2192	29	27	<	<	X
ajrhss-2192	29	28	1	1	NUM
ajrhss-2192	29	29	\	\	NOUN
ajrhss-2192	29	30	)	)	PUNCT
ajrhss-2192	29	31	)	)	PUNCT
ajrhss-2192	29	32	.	.	PUNCT
ajrhss-2192	30	1	the	the	DET
ajrhss-2192	30	2	graph	graph	NOUN
ajrhss-2192	30	3	is	be	AUX
ajrhss-2192	30	4	smooth	smooth	ADJ
ajrhss-2192	30	5	and	and	CCONJ
ajrhss-2192	30	6	continuous	continuous	ADJ
ajrhss-2192	30	7	,	,	PUNCT
ajrhss-2192	30	8	with	with	ADP
ajrhss-2192	30	9	no	no	DET
ajrhss-2192	30	10	breaks	break	NOUN
ajrhss-2192	30	11	or	or	CCONJ
ajrhss-2192	30	12	holes	hole	NOUN
ajrhss-2192	30	13	.	.	PUNCT
ajrhss-2192	31	1	for	for	ADP
ajrhss-2192	31	2	\	\	PROPN
ajrhss-2192	31	3	(	(	PUNCT
ajrhss-2192	31	4	b	b	X
ajrhss-2192	31	5	>	>	SYM
ajrhss-2192	31	6	1	1	NUM
ajrhss-2192	31	7	\	\	NOUN
ajrhss-2192	31	8	)	)	PUNCT
ajrhss-2192	31	9	,	,	PUNCT
ajrhss-2192	31	10	as	as	ADP
ajrhss-2192	31	11	\	\	PROPN
ajrhss-2192	31	12	(	(	PUNCT
ajrhss-2192	31	13	x	x	SYM
ajrhss-2192	31	14	\	\	ADJ
ajrhss-2192	31	15	)	)	PUNCT
ajrhss-2192	31	16	increases	increase	NOUN
ajrhss-2192	31	17	,	,	PUNCT
ajrhss-2192	31	18	\	\	PROPN
ajrhss-2192	31	19	(	(	PUNCT
ajrhss-2192	31	20	f(x	f(x	PROPN
ajrhss-2192	31	21	)	)	PUNCT
ajrhss-2192	31	22	\	\	NOUN
ajrhss-2192	31	23	)	)	PUNCT
ajrhss-2192	31	24	increases	increase	VERB
ajrhss-2192	31	25	rapidly	rapidly	ADV
ajrhss-2192	31	26	.	.	PUNCT
ajrhss-2192	32	1	for	for	ADP
ajrhss-2192	32	2	\	\	PROPN
ajrhss-2192	32	3	(	(	PUNCT
ajrhss-2192	32	4	0	0	NUM
ajrhss-2192	32	5	<	<	X
ajrhss-2192	32	6	b	b	X
ajrhss-2192	32	7	<	<	X
ajrhss-2192	32	8	1	1	NUM
ajrhss-2192	32	9	\	\	NOUN
ajrhss-2192	32	10	)	)	PUNCT
ajrhss-2192	32	11	,	,	PUNCT
ajrhss-2192	32	12	as	as	ADP
ajrhss-2192	32	13	\	\	PROPN
ajrhss-2192	32	14	(	(	PUNCT
ajrhss-2192	32	15	x	x	SYM
ajrhss-2192	32	16	\	\	ADJ
ajrhss-2192	32	17	)	)	PUNCT
ajrhss-2192	32	18	increases	increase	NOUN
ajrhss-2192	32	19	,	,	PUNCT
ajrhss-2192	32	20	\	\	PROPN
ajrhss-2192	32	21	(	(	PUNCT
ajrhss-2192	32	22	f(x	f(x	PROPN
ajrhss-2192	32	23	)	)	PUNCT
ajrhss-2192	32	24	\	\	NOUN
ajrhss-2192	32	25	)	)	PUNCT
ajrhss-2192	32	26	decreases	decrease	VERB
ajrhss-2192	32	27	rapidly	rapidly	ADV
ajrhss-2192	32	28	.	.	PUNCT
ajrhss-2192	33	1	the	the	DET
ajrhss-2192	33	2	natural	natural	ADJ
ajrhss-2192	33	3	exponential	exponential	ADJ
ajrhss-2192	33	4	function	function	NOUN
ajrhss-2192	33	5	when	when	SCONJ
ajrhss-2192	33	6	\	\	PROPN
ajrhss-2192	33	7	(	(	PUNCT
ajrhss-2192	33	8	b	b	X
ajrhss-2192	33	9	=	=	SYM
ajrhss-2192	33	10	e	e	NOUN
ajrhss-2192	33	11	\	\	PROPN
ajrhss-2192	33	12	)	)	PUNCT
ajrhss-2192	33	13	(	(	PUNCT
ajrhss-2192	33	14	where	where	SCONJ
ajrhss-2192	33	15	\	\	PROPN
ajrhss-2192	33	16	(	(	PUNCT
ajrhss-2192	33	17	e	e	PROPN
ajrhss-2192	33	18	\approx	\approx	PROPN
ajrhss-2192	33	19	2.71828	2.71828	NUM
ajrhss-2192	33	20	\	\	NOUN
ajrhss-2192	33	21	)	)	PUNCT
ajrhss-2192	33	22	)	)	PUNCT
ajrhss-2192	33	23	,	,	PUNCT
ajrhss-2192	33	24	the	the	DET
ajrhss-2192	33	25	function	function	NOUN
ajrhss-2192	33	26	is	be	AUX
ajrhss-2192	33	27	called	call	VERB
ajrhss-2192	33	28	the	the	DET
ajrhss-2192	33	29	natural	natural	ADJ
ajrhss-2192	33	30	exponential	exponential	ADJ
ajrhss-2192	33	31	function	function	NOUN
ajrhss-2192	33	32	:	:	PUNCT
ajrhss-2192	34	1	\	\	PROPN
ajrhss-2192	34	2	[	[	PUNCT
ajrhss-2192	34	3	f(x	f(x	PROPN
ajrhss-2192	34	4	)	)	PUNCT
ajrhss-2192	34	5	=	=	PUNCT
ajrhss-2192	34	6	e^x	e^x	NOUN
ajrhss-2192	34	7	\	\	NOUN
ajrhss-2192	34	8	]	]	PUNCT
ajrhss-2192	34	9	this	this	DET
ajrhss-2192	34	10	function	function	NOUN
ajrhss-2192	34	11	has	have	VERB
ajrhss-2192	34	12	unique	unique	ADJ
ajrhss-2192	34	13	properties	property	NOUN
ajrhss-2192	34	14	and	and	CCONJ
ajrhss-2192	34	15	is	be	AUX
ajrhss-2192	34	16	often	often	ADV
ajrhss-2192	34	17	used	use	VERB
ajrhss-2192	34	18	in	in	ADP
ajrhss-2192	34	19	calculus	calculus	NOUN
ajrhss-2192	34	20	and	and	CCONJ
ajrhss-2192	34	21	higher	high	ADJ
ajrhss-2192	34	22	mathematics	mathematic	NOUN
ajrhss-2192	34	23	.	.	PUNCT
ajrhss-2192	35	1	applications	application	NOUN
ajrhss-2192	35	2	of	of	ADP
ajrhss-2192	35	3	exponential	exponential	ADJ
ajrhss-2192	35	4	functions	function	NOUN
ajrhss-2192	35	5	1	1	NUM
ajrhss-2192	35	6	.	.	PUNCT
ajrhss-2192	35	7	biology	biology	NOUN
ajrhss-2192	35	8	:	:	PUNCT
ajrhss-2192	35	9	modeling	model	VERB
ajrhss-2192	35	10	population	population	NOUN
ajrhss-2192	35	11	growth	growth	NOUN
ajrhss-2192	35	12	,	,	PUNCT
ajrhss-2192	35	13	where	where	SCONJ
ajrhss-2192	35	14	the	the	DET
ajrhss-2192	35	15	rate	rate	NOUN
ajrhss-2192	35	16	of	of	ADP
ajrhss-2192	35	17	population	population	NOUN
ajrhss-2192	35	18	increase	increase	NOUN
ajrhss-2192	35	19	is	be	AUX
ajrhss-2192	35	20	proportional	proportional	ADJ
ajrhss-2192	35	21	to	to	ADP
ajrhss-2192	35	22	the	the	DET
ajrhss-2192	35	23	current	current	ADJ
ajrhss-2192	35	24	population	population	NOUN
ajrhss-2192	35	25	size	size	NOUN
ajrhss-2192	35	26	.	.	PUNCT
ajrhss-2192	36	1	2	2	X
ajrhss-2192	36	2	.	.	X
ajrhss-2192	36	3	finance	finance	NOUN
ajrhss-2192	36	4	:	:	PUNCT
ajrhss-2192	36	5	calculating	calculate	VERB
ajrhss-2192	36	6	compound	compound	NOUN
ajrhss-2192	36	7	interest	interest	NOUN
ajrhss-2192	36	8	,	,	PUNCT
ajrhss-2192	36	9	where	where	SCONJ
ajrhss-2192	36	10	the	the	DET
ajrhss-2192	36	11	amount	amount	NOUN
ajrhss-2192	36	12	of	of	ADP
ajrhss-2192	36	13	interest	interest	NOUN
ajrhss-2192	36	14	earned	earn	VERB
ajrhss-2192	36	15	grows	grow	VERB
ajrhss-2192	36	16	exponentially	exponentially	ADV
ajrhss-2192	36	17	over	over	ADP
ajrhss-2192	36	18	time	time	NOUN
ajrhss-2192	36	19	.	.	PUNCT
ajrhss-2192	37	1	3	3	X
ajrhss-2192	37	2	.	.	X
ajrhss-2192	37	3	physics	physics	NOUN
ajrhss-2192	37	4	:	:	PUNCT
ajrhss-2192	37	5	describing	describe	VERB
ajrhss-2192	37	6	radioactive	radioactive	ADJ
ajrhss-2192	37	7	decay	decay	NOUN
ajrhss-2192	37	8	,	,	PUNCT
ajrhss-2192	37	9	where	where	SCONJ
ajrhss-2192	37	10	the	the	DET
ajrhss-2192	37	11	quantity	quantity	NOUN
ajrhss-2192	37	12	of	of	ADP
ajrhss-2192	37	13	a	a	DET
ajrhss-2192	37	14	radioactive	radioactive	ADJ
ajrhss-2192	37	15	substance	substance	NOUN
ajrhss-2192	37	16	decreases	decrease	VERB
ajrhss-2192	37	17	exponentially	exponentially	ADV
ajrhss-2192	37	18	over	over	ADP
ajrhss-2192	37	19	time	time	NOUN
ajrhss-2192	37	20	.	.	PUNCT
ajrhss-2192	38	1	4	4	X
ajrhss-2192	38	2	.	.	X
ajrhss-2192	38	3	medicine	medicine	NOUN
ajrhss-2192	38	4	:	:	PUNCT
ajrhss-2192	38	5	modeling	model	VERB
ajrhss-2192	38	6	the	the	DET
ajrhss-2192	38	7	spread	spread	NOUN
ajrhss-2192	38	8	of	of	ADP
ajrhss-2192	38	9	diseases	disease	NOUN
ajrhss-2192	38	10	or	or	CCONJ
ajrhss-2192	38	11	the	the	DET
ajrhss-2192	38	12	decay	decay	NOUN
ajrhss-2192	38	13	of	of	ADP
ajrhss-2192	38	14	drug	drug	NOUN
ajrhss-2192	38	15	concentration	concentration	NOUN
ajrhss-2192	38	16	in	in	ADP
ajrhss-2192	38	17	the	the	DET
ajrhss-2192	38	18	bloodstream	bloodstream	NOUN
ajrhss-2192	38	19	.	.	PUNCT
ajrhss-2192	39	1	examples	example	NOUN
ajrhss-2192	39	2	american	american	PROPN
ajrhss-2192	39	3	journal	journal	PROPN
ajrhss-2192	39	4	of	of	ADP
ajrhss-2192	39	5	research	research	NOUN
ajrhss-2192	39	6	in	in	ADP
ajrhss-2192	39	7	humanities	humanity	NOUN
ajrhss-2192	39	8	and	and	CCONJ
ajrhss-2192	39	9	social	social	ADJ
ajrhss-2192	39	10	sciences	science	NOUN
ajrhss-2192	39	11	volume	volume	NOUN
ajrhss-2192	39	12	25	25	NUM
ajrhss-2192	39	13	june	june	PROPN
ajrhss-2192	39	14	2024	2024	NUM
ajrhss-2192	39	15	p	p	NOUN
ajrhss-2192	39	16	a	a	PRON
ajrhss-2192	39	17	g	g	NOUN
ajrhss-2192	39	18	e	e	NOUN
ajrhss-2192	40	1	|	|	ADV
ajrhss-2192	40	2	32	32	NUM
ajrhss-2192	40	3	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	40	4	1	1	NUM
ajrhss-2192	40	5	.	.	PUNCT
ajrhss-2192	40	6	exponential	exponential	ADJ
ajrhss-2192	40	7	growth	growth	NOUN
ajrhss-2192	40	8	:	:	PUNCT
ajrhss-2192	41	1	\	\	PROPN
ajrhss-2192	41	2	[	[	PUNCT
ajrhss-2192	41	3	f(x	f(x	PROPN
ajrhss-2192	41	4	)	)	PUNCT
ajrhss-2192	41	5	=	=	SYM
ajrhss-2192	41	6	2	2	NUM
ajrhss-2192	41	7	\cdot	\cdot	NOUN
ajrhss-2192	41	8	3^x	3^x	NUM
ajrhss-2192	41	9	\	\	NOUN
ajrhss-2192	41	10	]	]	PUNCT
ajrhss-2192	41	11	here	here	ADV
ajrhss-2192	41	12	,	,	PUNCT
ajrhss-2192	41	13	the	the	DET
ajrhss-2192	41	14	initial	initial	ADJ
ajrhss-2192	41	15	value	value	NOUN
ajrhss-2192	41	16	\	\	PROPN
ajrhss-2192	41	17	(	(	PUNCT
ajrhss-2192	41	18	a	a	DET
ajrhss-2192	41	19	=	=	SYM
ajrhss-2192	41	20	2	2	NUM
ajrhss-2192	41	21	\	\	NOUN
ajrhss-2192	41	22	)	)	PUNCT
ajrhss-2192	41	23	and	and	CCONJ
ajrhss-2192	41	24	the	the	DET
ajrhss-2192	41	25	base	base	NOUN
ajrhss-2192	41	26	\	\	PROPN
ajrhss-2192	41	27	(	(	PUNCT
ajrhss-2192	41	28	b	b	X
ajrhss-2192	41	29	=	=	SYM
ajrhss-2192	41	30	3	3	NUM
ajrhss-2192	41	31	\	\	NOUN
ajrhss-2192	41	32	)	)	PUNCT
ajrhss-2192	41	33	.	.	PUNCT
ajrhss-2192	42	1	the	the	DET
ajrhss-2192	42	2	function	function	NOUN
ajrhss-2192	42	3	grows	grow	VERB
ajrhss-2192	42	4	exponentially	exponentially	ADV
ajrhss-2192	42	5	as	as	ADP
ajrhss-2192	42	6	\	\	PROPN
ajrhss-2192	42	7	(	(	PUNCT
ajrhss-2192	42	8	x	x	SYM
ajrhss-2192	42	9	\	\	ADJ
ajrhss-2192	42	10	)	)	PUNCT
ajrhss-2192	42	11	increases	increase	NOUN
ajrhss-2192	42	12	.	.	PUNCT
ajrhss-2192	43	1	2	2	X
ajrhss-2192	43	2	.	.	X
ajrhss-2192	43	3	exponential	exponential	ADJ
ajrhss-2192	43	4	decay	decay	NOUN
ajrhss-2192	43	5	:	:	PUNCT
ajrhss-2192	44	1	\	\	PROPN
ajrhss-2192	44	2	[	[	PUNCT
ajrhss-2192	44	3	f(x	f(x	PROPN
ajrhss-2192	44	4	)	)	PUNCT
ajrhss-2192	44	5	=	=	NOUN
ajrhss-2192	44	6	5	5	NUM
ajrhss-2192	44	7	\cdot	\cdot	NOUN
ajrhss-2192	44	8	(	(	PUNCT
ajrhss-2192	44	9	0.5)^x	0.5)^x	NOUN
ajrhss-2192	44	10	\	\	NOUN
ajrhss-2192	44	11	]	]	PUNCT
ajrhss-2192	44	12	here	here	ADV
ajrhss-2192	44	13	,	,	PUNCT
ajrhss-2192	44	14	the	the	DET
ajrhss-2192	44	15	initial	initial	ADJ
ajrhss-2192	44	16	value	value	NOUN
ajrhss-2192	44	17	\	\	PROPN
ajrhss-2192	44	18	(	(	PUNCT
ajrhss-2192	44	19	a	a	DET
ajrhss-2192	44	20	=	=	SYM
ajrhss-2192	44	21	5	5	NUM
ajrhss-2192	44	22	\	\	NOUN
ajrhss-2192	44	23	)	)	PUNCT
ajrhss-2192	44	24	and	and	CCONJ
ajrhss-2192	44	25	the	the	DET
ajrhss-2192	44	26	base	base	NOUN
ajrhss-2192	44	27	\	\	PROPN
ajrhss-2192	44	28	(	(	PUNCT
ajrhss-2192	44	29	b	b	NOUN
ajrhss-2192	44	30	=	=	SYM
ajrhss-2192	44	31	0.5	0.5	NUM
ajrhss-2192	44	32	\	\	NOUN
ajrhss-2192	44	33	)	)	PUNCT
ajrhss-2192	44	34	.	.	PUNCT
ajrhss-2192	45	1	the	the	DET
ajrhss-2192	45	2	function	function	NOUN
ajrhss-2192	45	3	decays	decay	VERB
ajrhss-2192	45	4	exponentially	exponentially	ADV
ajrhss-2192	45	5	as	as	ADP
ajrhss-2192	45	6	\	\	PROPN
ajrhss-2192	45	7	(	(	PUNCT
ajrhss-2192	45	8	x	x	SYM
ajrhss-2192	45	9	\	\	ADJ
ajrhss-2192	45	10	)	)	PUNCT
ajrhss-2192	45	11	increases	increase	NOUN
ajrhss-2192	45	12	.	.	PUNCT
ajrhss-2192	46	1	calculus	calculus	NOUN
ajrhss-2192	46	2	with	with	ADP
ajrhss-2192	46	3	exponential	exponential	ADJ
ajrhss-2192	46	4	functions	function	NOUN
ajrhss-2192	46	5	the	the	DET
ajrhss-2192	46	6	derivative	derivative	NOUN
ajrhss-2192	46	7	of	of	ADP
ajrhss-2192	46	8	\	\	PROPN
ajrhss-2192	46	9	(	(	PUNCT
ajrhss-2192	46	10	e^x	e^x	PROPN
ajrhss-2192	46	11	\	\	PROPN
ajrhss-2192	46	12	)	)	PUNCT
ajrhss-2192	46	13	is	be	AUX
ajrhss-2192	46	14	\	\	NOUN
ajrhss-2192	46	15	(	(	PUNCT
ajrhss-2192	46	16	e^x	e^x	NOUN
ajrhss-2192	46	17	\	\	PROPN
ajrhss-2192	46	18	)	)	PUNCT
ajrhss-2192	46	19	.	.	PUNCT
ajrhss-2192	47	1	the	the	DET
ajrhss-2192	47	2	integral	integral	NOUN
ajrhss-2192	47	3	of	of	ADP
ajrhss-2192	47	4	\	\	PROPN
ajrhss-2192	47	5	(	(	PUNCT
ajrhss-2192	47	6	e^x	e^x	PROPN
ajrhss-2192	47	7	\	\	PROPN
ajrhss-2192	47	8	)	)	PUNCT
ajrhss-2192	47	9	is	be	AUX
ajrhss-2192	47	10	\	\	NOUN
ajrhss-2192	47	11	(	(	PUNCT
ajrhss-2192	47	12	e^x	e^x	NOUN
ajrhss-2192	47	13	+	+	CCONJ
ajrhss-2192	47	14	c	c	NOUN
ajrhss-2192	47	15	\	\	NOUN
ajrhss-2192	47	16	)	)	PUNCT
ajrhss-2192	47	17	,	,	PUNCT
ajrhss-2192	47	18	where	where	SCONJ
ajrhss-2192	47	19	\	\	PROPN
ajrhss-2192	47	20	(	(	PUNCT
ajrhss-2192	47	21	c	c	NOUN
ajrhss-2192	47	22	\	\	PROPN
ajrhss-2192	47	23	)	)	PUNCT
ajrhss-2192	47	24	is	be	AUX
ajrhss-2192	47	25	the	the	DET
ajrhss-2192	47	26	constant	constant	ADJ
ajrhss-2192	47	27	of	of	ADP
ajrhss-2192	47	28	integration	integration	NOUN
ajrhss-2192	47	29	.	.	PUNCT
ajrhss-2192	48	1	exponential	exponential	ADJ
ajrhss-2192	48	2	functions	function	NOUN
ajrhss-2192	48	3	are	be	AUX
ajrhss-2192	48	4	useful	useful	ADJ
ajrhss-2192	48	5	in	in	ADP
ajrhss-2192	48	6	solving	solve	VERB
ajrhss-2192	48	7	differential	differential	ADJ
ajrhss-2192	48	8	equations	equation	NOUN
ajrhss-2192	48	9	where	where	SCONJ
ajrhss-2192	48	10	the	the	DET
ajrhss-2192	48	11	rate	rate	NOUN
ajrhss-2192	48	12	of	of	ADP
ajrhss-2192	48	13	change	change	NOUN
ajrhss-2192	48	14	of	of	ADP
ajrhss-2192	48	15	a	a	DET
ajrhss-2192	48	16	quantity	quantity	NOUN
ajrhss-2192	48	17	is	be	AUX
ajrhss-2192	48	18	proportional	proportional	ADJ
ajrhss-2192	48	19	to	to	ADP
ajrhss-2192	48	20	the	the	DET
ajrhss-2192	48	21	quantity	quantity	NOUN
ajrhss-2192	48	22	itsel	itsel	VERB
ajrhss-2192	48	23	exponential	exponential	ADJ
ajrhss-2192	48	24	growth	growth	NOUN
ajrhss-2192	48	25	and	and	CCONJ
ajrhss-2192	48	26	decay	decay	NOUN
ajrhss-2192	48	27	models	model	NOUN
ajrhss-2192	48	28	exponential	exponential	ADJ
ajrhss-2192	48	29	growth	growth	NOUN
ajrhss-2192	48	30	model	model	NOUN
ajrhss-2192	48	31	:	:	PUNCT
ajrhss-2192	49	1	\	\	PROPN
ajrhss-2192	49	2	(	(	PUNCT
ajrhss-2192	49	3	p(t	p(t	NOUN
ajrhss-2192	49	4	)	)	PUNCT
ajrhss-2192	49	5	=	=	PUNCT
ajrhss-2192	49	6	p_0	p_0	NOUN
ajrhss-2192	49	7	e^{rt	e^{rt	PROPN
ajrhss-2192	49	8	}	}	PUNCT
ajrhss-2192	49	9	\	\	ADJ
ajrhss-2192	49	10	)	)	PUNCT
ajrhss-2192	49	11	\	\	PROPN
ajrhss-2192	49	12	(	(	PUNCT
ajrhss-2192	49	13	p(t	p(t	NOUN
ajrhss-2192	49	14	)	)	PUNCT
ajrhss-2192	50	1	\	\	NOUN
ajrhss-2192	50	2	):	):	PUNCT
ajrhss-2192	50	3	population	population	NOUN
ajrhss-2192	50	4	at	at	ADP
ajrhss-2192	50	5	time	time	NOUN
ajrhss-2192	50	6	\	\	PROPN
ajrhss-2192	50	7	(	(	PUNCT
ajrhss-2192	50	8	t	t	NOUN
ajrhss-2192	50	9	\	\	PROPN
ajrhss-2192	50	10	)	)	PUNCT
ajrhss-2192	51	1	\	\	PROPN
ajrhss-2192	51	2	(	(	PUNCT
ajrhss-2192	51	3	p_0	p_0	PROPN
ajrhss-2192	51	4	\	\	NOUN
ajrhss-2192	51	5	):	):	PUNCT
ajrhss-2192	51	6	initial	initial	ADJ
ajrhss-2192	51	7	population	population	NOUN
ajrhss-2192	51	8	\	\	PROPN
ajrhss-2192	51	9	(	(	PUNCT
ajrhss-2192	51	10	r	r	NOUN
ajrhss-2192	51	11	\	\	NOUN
ajrhss-2192	51	12	):	):	PUNCT
ajrhss-2192	51	13	growth	growth	NOUN
ajrhss-2192	51	14	rate	rate	NOUN
ajrhss-2192	51	15	\	\	PROPN
ajrhss-2192	51	16	(	(	PUNCT
ajrhss-2192	51	17	t	t	NOUN
ajrhss-2192	51	18	\	\	PROPN
ajrhss-2192	51	19	):	):	PUNCT
ajrhss-2192	51	20	time	time	NOUN
ajrhss-2192	51	21	exponential	exponential	ADJ
ajrhss-2192	51	22	decay	decay	NOUN
ajrhss-2192	51	23	model	model	NOUN
ajrhss-2192	51	24	:	:	PUNCT
ajrhss-2192	51	25	\	\	PROPN
ajrhss-2192	51	26	(	(	PUNCT
ajrhss-2192	51	27	n(t	n(t	PROPN
ajrhss-2192	51	28	)	)	PUNCT
ajrhss-2192	51	29	=	=	SYM
ajrhss-2192	51	30	n_0	n_0	PROPN
ajrhss-2192	51	31	e^{-kt	e^{-kt	PROPN
ajrhss-2192	51	32	}	}	PUNCT
ajrhss-2192	51	33	\	\	ADJ
ajrhss-2192	51	34	)	)	PUNCT
ajrhss-2192	51	35	\	\	PROPN
ajrhss-2192	51	36	(	(	PUNCT
ajrhss-2192	51	37	n(t	n(t	PROPN
ajrhss-2192	51	38	)	)	PUNCT
ajrhss-2192	51	39	\	\	NOUN
ajrhss-2192	51	40	):	):	PUNCT
ajrhss-2192	51	41	quantity	quantity	NOUN
ajrhss-2192	51	42	at	at	ADP
ajrhss-2192	51	43	time	time	NOUN
ajrhss-2192	51	44	\	\	PROPN
ajrhss-2192	51	45	(	(	PUNCT
ajrhss-2192	51	46	t	t	NOUN
ajrhss-2192	51	47	\	\	PROPN
ajrhss-2192	51	48	)	)	PUNCT
ajrhss-2192	52	1	\	\	PROPN
ajrhss-2192	52	2	(	(	PUNCT
ajrhss-2192	52	3	n_0	n_0	PROPN
ajrhss-2192	52	4	\	\	PROPN
ajrhss-2192	52	5	):	):	PUNCT
ajrhss-2192	52	6	initial	initial	ADJ
ajrhss-2192	52	7	quantity	quantity	NOUN
ajrhss-2192	52	8	\	\	PROPN
ajrhss-2192	52	9	(	(	PUNCT
ajrhss-2192	52	10	k	k	PROPN
ajrhss-2192	52	11	\	\	PROPN
ajrhss-2192	52	12	):	):	PUNCT
ajrhss-2192	52	13	decay	decay	VERB
ajrhss-2192	52	14	constant	constant	ADJ
ajrhss-2192	52	15	\	\	PROPN
ajrhss-2192	52	16	(	(	PUNCT
ajrhss-2192	52	17	t	t	NOUN
ajrhss-2192	52	18	\	\	PROPN
ajrhss-2192	52	19	):	):	PUNCT
ajrhss-2192	52	20	time	time	NOUN
ajrhss-2192	52	21	understanding	understand	VERB
ajrhss-2192	52	22	these	these	DET
ajrhss-2192	52	23	concepts	concept	NOUN
ajrhss-2192	52	24	helps	help	VERB
ajrhss-2192	52	25	in	in	ADP
ajrhss-2192	52	26	analyzing	analyze	VERB
ajrhss-2192	52	27	and	and	CCONJ
ajrhss-2192	52	28	interpreting	interpret	VERB
ajrhss-2192	52	29	various	various	ADJ
ajrhss-2192	52	30	natural	natural	ADJ
ajrhss-2192	52	31	and	and	CCONJ
ajrhss-2192	52	32	financial	financial	ADJ
ajrhss-2192	52	33	phenomena	phenomenon	NOUN
ajrhss-2192	52	34	that	that	PRON
ajrhss-2192	52	35	exhibit	exhibit	VERB
ajrhss-2192	52	36	exponential	exponential	ADJ
ajrhss-2192	52	37	behavior	behavior	NOUN
ajrhss-2192	52	38	.	.	PUNCT
ajrhss-2192	53	1	exponential	exponential	ADJ
ajrhss-2192	53	2	functions	function	NOUN
ajrhss-2192	53	3	play	play	VERB
ajrhss-2192	53	4	a	a	DET
ajrhss-2192	53	5	critical	critical	ADJ
ajrhss-2192	53	6	role	role	NOUN
ajrhss-2192	53	7	in	in	ADP
ajrhss-2192	53	8	mathematics	mathematic	NOUN
ajrhss-2192	53	9	due	due	ADP
ajrhss-2192	53	10	to	to	ADP
ajrhss-2192	53	11	their	their	PRON
ajrhss-2192	53	12	unique	unique	ADJ
ajrhss-2192	53	13	properties	property	NOUN
ajrhss-2192	53	14	and	and	CCONJ
ajrhss-2192	53	15	wide	wide	ADJ
ajrhss-2192	53	16	range	range	NOUN
ajrhss-2192	53	17	of	of	ADP
ajrhss-2192	53	18	applications	application	NOUN
ajrhss-2192	53	19	.	.	PUNCT
ajrhss-2192	54	1	here	here	ADV
ajrhss-2192	54	2	are	be	AUX
ajrhss-2192	54	3	several	several	ADJ
ajrhss-2192	54	4	key	key	ADJ
ajrhss-2192	54	5	aspects	aspect	NOUN
ajrhss-2192	54	6	of	of	ADP
ajrhss-2192	54	7	their	their	PRON
ajrhss-2192	54	8	significance	significance	NOUN
ajrhss-2192	54	9	:	:	PUNCT
ajrhss-2192	54	10	fundamental	fundamental	ADJ
ajrhss-2192	54	11	properties	property	NOUN
ajrhss-2192	54	12	1	1	NUM
ajrhss-2192	54	13	.	.	PUNCT
ajrhss-2192	54	14	continuous	continuous	ADJ
ajrhss-2192	54	15	growth	growth	NOUN
ajrhss-2192	54	16	and	and	CCONJ
ajrhss-2192	54	17	decay	decay	NOUN
ajrhss-2192	54	18	:	:	PUNCT
ajrhss-2192	54	19	exponential	exponential	ADJ
ajrhss-2192	54	20	functions	function	NOUN
ajrhss-2192	54	21	model	model	NOUN
ajrhss-2192	54	22	processes	process	NOUN
ajrhss-2192	54	23	that	that	PRON
ajrhss-2192	54	24	grow	grow	VERB
ajrhss-2192	54	25	or	or	CCONJ
ajrhss-2192	54	26	decay	decay	VERB
ajrhss-2192	54	27	at	at	ADP
ajrhss-2192	54	28	a	a	DET
ajrhss-2192	54	29	rate	rate	NOUN
ajrhss-2192	54	30	proportional	proportional	ADJ
ajrhss-2192	54	31	to	to	ADP
ajrhss-2192	54	32	their	their	PRON
ajrhss-2192	54	33	current	current	ADJ
ajrhss-2192	54	34	value	value	NOUN
ajrhss-2192	54	35	.	.	PUNCT
ajrhss-2192	55	1	this	this	DET
ajrhss-2192	55	2	characteristic	characteristic	NOUN
ajrhss-2192	55	3	makes	make	VERB
ajrhss-2192	55	4	them	they	PRON
ajrhss-2192	55	5	essential	essential	ADJ
ajrhss-2192	55	6	in	in	ADP
ajrhss-2192	55	7	describing	describe	VERB
ajrhss-2192	55	8	natural	natural	ADJ
ajrhss-2192	55	9	phenomena	phenomenon	NOUN
ajrhss-2192	55	10	like	like	ADP
ajrhss-2192	55	11	population	population	NOUN
ajrhss-2192	55	12	growth	growth	NOUN
ajrhss-2192	55	13	,	,	PUNCT
ajrhss-2192	55	14	radioactive	radioactive	ADJ
ajrhss-2192	55	15	decay	decay	NOUN
ajrhss-2192	55	16	,	,	PUNCT
ajrhss-2192	55	17	and	and	CCONJ
ajrhss-2192	55	18	interest	interest	NOUN
ajrhss-2192	55	19	calculations	calculation	NOUN
ajrhss-2192	55	20	.	.	PUNCT
ajrhss-2192	56	1	2	2	X
ajrhss-2192	56	2	.	.	X
ajrhss-2192	56	3	derivative	derivative	ADJ
ajrhss-2192	56	4	and	and	CCONJ
ajrhss-2192	56	5	integral	integral	ADJ
ajrhss-2192	56	6	properties	property	NOUN
ajrhss-2192	56	7	:	:	PUNCT
ajrhss-2192	56	8	the	the	DET
ajrhss-2192	56	9	natural	natural	ADJ
ajrhss-2192	56	10	exponential	exponential	ADJ
ajrhss-2192	56	11	function	function	NOUN
ajrhss-2192	56	12	\	\	PROPN
ajrhss-2192	56	13	(	(	PUNCT
ajrhss-2192	56	14	e^x	e^x	PROPN
ajrhss-2192	56	15	\	\	PROPN
ajrhss-2192	56	16	)	)	PUNCT
ajrhss-2192	56	17	is	be	AUX
ajrhss-2192	56	18	unique	unique	ADJ
ajrhss-2192	56	19	in	in	ADP
ajrhss-2192	56	20	that	that	SCONJ
ajrhss-2192	56	21	its	its	PRON
ajrhss-2192	56	22	derivative	derivative	ADJ
ajrhss-2192	56	23	and	and	CCONJ
ajrhss-2192	56	24	integral	integral	ADJ
ajrhss-2192	56	25	are	be	AUX
ajrhss-2192	56	26	the	the	DET
ajrhss-2192	56	27	same	same	ADJ
ajrhss-2192	56	28	,	,	PUNCT
ajrhss-2192	56	29	\	\	PROPN
ajrhss-2192	56	30	(	(	PUNCT
ajrhss-2192	56	31	\frac{d}{dx	\frac{d}{dx	NOUN
ajrhss-2192	56	32	}	}	PUNCT
ajrhss-2192	56	33	e^x	e^x	NOUN
ajrhss-2192	56	34	=	=	SYM
ajrhss-2192	56	35	e^x	e^x	NOUN
ajrhss-2192	56	36	\	\	PROPN
ajrhss-2192	56	37	)	)	PUNCT
ajrhss-2192	56	38	and	and	CCONJ
ajrhss-2192	56	39	\	\	PROPN
ajrhss-2192	56	40	(	(	PUNCT
ajrhss-2192	56	41	\int	\int	NOUN
ajrhss-2192	56	42	e^x	e^x	PROPN
ajrhss-2192	56	43	\	\	PROPN
ajrhss-2192	56	44	,	,	PUNCT
ajrhss-2192	56	45	dx	dx	PROPN
ajrhss-2192	57	1	=	=	PUNCT
ajrhss-2192	57	2	e^x	e^x	PROPN
ajrhss-2192	57	3	+	+	CCONJ
ajrhss-2192	57	4	c	c	NOUN
ajrhss-2192	57	5	\	\	NOUN
ajrhss-2192	57	6	)	)	PUNCT
ajrhss-2192	57	7	.	.	PUNCT
ajrhss-2192	58	1	american	american	PROPN
ajrhss-2192	58	2	journal	journal	PROPN
ajrhss-2192	58	3	of	of	ADP
ajrhss-2192	58	4	research	research	NOUN
ajrhss-2192	58	5	in	in	ADP
ajrhss-2192	58	6	humanities	humanity	NOUN
ajrhss-2192	58	7	and	and	CCONJ
ajrhss-2192	58	8	social	social	ADJ
ajrhss-2192	58	9	sciences	science	NOUN
ajrhss-2192	58	10	volume	volume	NOUN
ajrhss-2192	58	11	25	25	NUM
ajrhss-2192	58	12	june	june	PROPN
ajrhss-2192	58	13	2024	2024	NUM
ajrhss-2192	58	14	p	p	NOUN
ajrhss-2192	58	15	a	a	DET
ajrhss-2192	58	16	g	g	NOUN
ajrhss-2192	58	17	e	e	NOUN
ajrhss-2192	58	18	|	|	ADV
ajrhss-2192	58	19	33	33	NUM
ajrhss-2192	58	20	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	58	21	this	this	DET
ajrhss-2192	58	22	property	property	NOUN
ajrhss-2192	58	23	simplifies	simplifie	NOUN
ajrhss-2192	58	24	solving	solve	VERB
ajrhss-2192	58	25	differential	differential	ADJ
ajrhss-2192	58	26	equations	equation	NOUN
ajrhss-2192	58	27	,	,	PUNCT
ajrhss-2192	58	28	particularly	particularly	ADV
ajrhss-2192	58	29	those	those	PRON
ajrhss-2192	58	30	modeling	model	VERB
ajrhss-2192	58	31	exponential	exponential	ADJ
ajrhss-2192	58	32	growth	growth	NOUN
ajrhss-2192	58	33	or	or	CCONJ
ajrhss-2192	58	34	decay	decay	NOUN
ajrhss-2192	58	35	.	.	PUNCT
ajrhss-2192	59	1	applications	application	NOUN
ajrhss-2192	59	2	in	in	ADP
ajrhss-2192	59	3	different	different	ADJ
ajrhss-2192	59	4	fields	field	NOUN
ajrhss-2192	59	5	1	1	NUM
ajrhss-2192	59	6	.	.	PUNCT
ajrhss-2192	60	1	calculus	calculus	NOUN
ajrhss-2192	60	2	:	:	PUNCT
ajrhss-2192	60	3	exponential	exponential	ADJ
ajrhss-2192	60	4	functions	function	NOUN
ajrhss-2192	60	5	are	be	AUX
ajrhss-2192	60	6	integral	integral	ADJ
ajrhss-2192	60	7	to	to	ADP
ajrhss-2192	60	8	solving	solve	VERB
ajrhss-2192	60	9	various	various	ADJ
ajrhss-2192	60	10	types	type	NOUN
ajrhss-2192	60	11	of	of	ADP
ajrhss-2192	60	12	differential	differential	ADJ
ajrhss-2192	60	13	equations	equation	NOUN
ajrhss-2192	60	14	.	.	PUNCT
ajrhss-2192	61	1	they	they	PRON
ajrhss-2192	61	2	are	be	AUX
ajrhss-2192	61	3	used	use	VERB
ajrhss-2192	61	4	in	in	ADP
ajrhss-2192	61	5	defining	define	VERB
ajrhss-2192	61	6	and	and	CCONJ
ajrhss-2192	61	7	working	work	VERB
ajrhss-2192	61	8	with	with	ADP
ajrhss-2192	61	9	the	the	DET
ajrhss-2192	61	10	exponential	exponential	ADJ
ajrhss-2192	61	11	function	function	NOUN
ajrhss-2192	61	12	,	,	PUNCT
ajrhss-2192	61	13	logarithmic	logarithmic	ADJ
ajrhss-2192	61	14	function	function	NOUN
ajrhss-2192	61	15	,	,	PUNCT
ajrhss-2192	61	16	and	and	CCONJ
ajrhss-2192	61	17	in	in	ADP
ajrhss-2192	61	18	the	the	DET
ajrhss-2192	61	19	computation	computation	NOUN
ajrhss-2192	61	20	of	of	ADP
ajrhss-2192	61	21	limits	limit	NOUN
ajrhss-2192	61	22	and	and	CCONJ
ajrhss-2192	61	23	series	series	NOUN
ajrhss-2192	61	24	.	.	PUNCT
ajrhss-2192	62	1	2	2	X
ajrhss-2192	62	2	.	.	X
ajrhss-2192	62	3	statistics	statistic	NOUN
ajrhss-2192	62	4	and	and	CCONJ
ajrhss-2192	62	5	probability	probability	NOUN
ajrhss-2192	62	6	:	:	PUNCT
ajrhss-2192	62	7	exponential	exponential	ADJ
ajrhss-2192	62	8	distributions	distribution	NOUN
ajrhss-2192	62	9	model	model	VERB
ajrhss-2192	62	10	the	the	DET
ajrhss-2192	62	11	time	time	NOUN
ajrhss-2192	62	12	between	between	ADP
ajrhss-2192	62	13	events	event	NOUN
ajrhss-2192	62	14	in	in	ADP
ajrhss-2192	62	15	a	a	DET
ajrhss-2192	62	16	poisson	poisson	NOUN
ajrhss-2192	62	17	process	process	NOUN
ajrhss-2192	62	18	,	,	PUNCT
ajrhss-2192	62	19	such	such	ADJ
ajrhss-2192	62	20	as	as	ADP
ajrhss-2192	62	21	the	the	DET
ajrhss-2192	62	22	time	time	NOUN
ajrhss-2192	62	23	between	between	ADP
ajrhss-2192	62	24	arrivals	arrival	NOUN
ajrhss-2192	62	25	at	at	ADP
ajrhss-2192	62	26	a	a	DET
ajrhss-2192	62	27	service	service	NOUN
ajrhss-2192	62	28	center	center	NOUN
ajrhss-2192	62	29	or	or	CCONJ
ajrhss-2192	62	30	the	the	DET
ajrhss-2192	62	31	time	time	NOUN
ajrhss-2192	62	32	until	until	ADP
ajrhss-2192	62	33	a	a	DET
ajrhss-2192	62	34	radioactive	radioactive	ADJ
ajrhss-2192	62	35	particle	particle	NOUN
ajrhss-2192	62	36	decays	decay	NOUN
ajrhss-2192	62	37	.	.	PUNCT
ajrhss-2192	63	1	they	they	PRON
ajrhss-2192	63	2	are	be	AUX
ajrhss-2192	63	3	used	use	VERB
ajrhss-2192	63	4	in	in	ADP
ajrhss-2192	63	5	survival	survival	NOUN
ajrhss-2192	63	6	analysis	analysis	NOUN
ajrhss-2192	63	7	and	and	CCONJ
ajrhss-2192	63	8	reliability	reliability	NOUN
ajrhss-2192	63	9	engineering	engineering	NOUN
ajrhss-2192	63	10	.	.	PUNCT
ajrhss-2192	64	1	3	3	X
ajrhss-2192	64	2	.	.	X
ajrhss-2192	64	3	physics	physics	NOUN
ajrhss-2192	64	4	:	:	PUNCT
ajrhss-2192	64	5	exponential	exponential	ADJ
ajrhss-2192	64	6	functions	function	NOUN
ajrhss-2192	64	7	describe	describe	VERB
ajrhss-2192	64	8	radioactive	radioactive	ADJ
ajrhss-2192	64	9	decay	decay	NOUN
ajrhss-2192	64	10	,	,	PUNCT
ajrhss-2192	64	11	cooling	cool	VERB
ajrhss-2192	64	12	processes	process	NOUN
ajrhss-2192	64	13	(	(	PUNCT
ajrhss-2192	64	14	newton	newton	PROPN
ajrhss-2192	64	15	's	's	PART
ajrhss-2192	64	16	law	law	NOUN
ajrhss-2192	64	17	of	of	ADP
ajrhss-2192	64	18	cooling	cooling	NOUN
ajrhss-2192	64	19	)	)	PUNCT
ajrhss-2192	64	20	,	,	PUNCT
ajrhss-2192	64	21	and	and	CCONJ
ajrhss-2192	64	22	charging	charge	VERB
ajrhss-2192	64	23	and	and	CCONJ
ajrhss-2192	64	24	discharging	discharge	VERB
ajrhss-2192	64	25	of	of	ADP
ajrhss-2192	64	26	capacitors	capacitor	NOUN
ajrhss-2192	64	27	(	(	PUNCT
ajrhss-2192	64	28	rc	rc	PROPN
ajrhss-2192	64	29	circuits	circuit	NOUN
ajrhss-2192	64	30	)	)	PUNCT
ajrhss-2192	64	31	.	.	PUNCT
ajrhss-2192	65	1	they	they	PRON
ajrhss-2192	65	2	also	also	ADV
ajrhss-2192	65	3	appear	appear	VERB
ajrhss-2192	65	4	in	in	ADP
ajrhss-2192	65	5	solutions	solution	NOUN
ajrhss-2192	65	6	to	to	ADP
ajrhss-2192	65	7	the	the	DET
ajrhss-2192	65	8	schrödinger	schrödinger	ADJ
ajrhss-2192	65	9	equation	equation	NOUN
ajrhss-2192	65	10	in	in	ADP
ajrhss-2192	65	11	quantum	quantum	ADJ
ajrhss-2192	65	12	mechanics	mechanic	NOUN
ajrhss-2192	65	13	.	.	PUNCT
ajrhss-2192	66	1	4	4	X
ajrhss-2192	66	2	.	.	X
ajrhss-2192	66	3	biology	biology	NOUN
ajrhss-2192	66	4	:	:	PUNCT
ajrhss-2192	66	5	exponential	exponential	ADJ
ajrhss-2192	66	6	growth	growth	NOUN
ajrhss-2192	66	7	models	model	NOUN
ajrhss-2192	66	8	are	be	AUX
ajrhss-2192	66	9	used	use	VERB
ajrhss-2192	66	10	to	to	PART
ajrhss-2192	66	11	describe	describe	VERB
ajrhss-2192	66	12	populations	population	NOUN
ajrhss-2192	66	13	under	under	ADP
ajrhss-2192	66	14	ideal	ideal	ADJ
ajrhss-2192	66	15	conditions	condition	NOUN
ajrhss-2192	66	16	where	where	SCONJ
ajrhss-2192	66	17	resources	resource	NOUN
ajrhss-2192	66	18	are	be	AUX
ajrhss-2192	66	19	unlimited	unlimited	ADJ
ajrhss-2192	66	20	.	.	PUNCT
ajrhss-2192	67	1	exponential	exponential	ADJ
ajrhss-2192	67	2	decay	decay	NOUN
ajrhss-2192	67	3	models	model	NOUN
ajrhss-2192	67	4	are	be	AUX
ajrhss-2192	67	5	used	use	VERB
ajrhss-2192	67	6	in	in	ADP
ajrhss-2192	67	7	pharmacokinetics	pharmacokinetic	NOUN
ajrhss-2192	67	8	to	to	PART
ajrhss-2192	67	9	describe	describe	VERB
ajrhss-2192	67	10	how	how	SCONJ
ajrhss-2192	67	11	drugs	drug	NOUN
ajrhss-2192	67	12	are	be	AUX
ajrhss-2192	67	13	metabolized	metabolize	VERB
ajrhss-2192	67	14	in	in	ADP
ajrhss-2192	67	15	the	the	DET
ajrhss-2192	67	16	body	body	NOUN
ajrhss-2192	67	17	.	.	PUNCT
ajrhss-2192	68	1	5	5	X
ajrhss-2192	68	2	.	.	X
ajrhss-2192	68	3	finance	finance	NOUN
ajrhss-2192	68	4	and	and	CCONJ
ajrhss-2192	68	5	economics	economic	NOUN
ajrhss-2192	68	6	:	:	PUNCT
ajrhss-2192	68	7	compound	compound	NOUN
ajrhss-2192	68	8	interest	interest	NOUN
ajrhss-2192	68	9	calculations	calculation	NOUN
ajrhss-2192	68	10	are	be	AUX
ajrhss-2192	68	11	based	base	VERB
ajrhss-2192	68	12	on	on	ADP
ajrhss-2192	68	13	exponential	exponential	ADJ
ajrhss-2192	68	14	functions	function	NOUN
ajrhss-2192	68	15	,	,	PUNCT
ajrhss-2192	68	16	modeling	model	VERB
ajrhss-2192	68	17	the	the	DET
ajrhss-2192	68	18	growth	growth	NOUN
ajrhss-2192	68	19	of	of	ADP
ajrhss-2192	68	20	investments	investment	NOUN
ajrhss-2192	68	21	over	over	ADP
ajrhss-2192	68	22	time	time	NOUN
ajrhss-2192	68	23	.	.	PUNCT
ajrhss-2192	69	1	they	they	PRON
ajrhss-2192	69	2	are	be	AUX
ajrhss-2192	69	3	used	use	VERB
ajrhss-2192	69	4	in	in	ADP
ajrhss-2192	69	5	models	model	NOUN
ajrhss-2192	69	6	of	of	ADP
ajrhss-2192	69	7	economic	economic	ADJ
ajrhss-2192	69	8	growth	growth	NOUN
ajrhss-2192	69	9	and	and	CCONJ
ajrhss-2192	69	10	in	in	ADP
ajrhss-2192	69	11	analyzing	analyze	VERB
ajrhss-2192	69	12	continuously	continuously	ADV
ajrhss-2192	69	13	compounded	compound	VERB
ajrhss-2192	69	14	interest	interest	NOUN
ajrhss-2192	69	15	.	.	PUNCT
ajrhss-2192	70	1	advanced	advanced	ADJ
ajrhss-2192	70	2	mathematical	mathematical	ADJ
ajrhss-2192	70	3	concepts	concept	NOUN
ajrhss-2192	70	4	1	1	NUM
ajrhss-2192	70	5	.	.	PUNCT
ajrhss-2192	71	1	complex	complex	ADJ
ajrhss-2192	71	2	analysis	analysis	NOUN
ajrhss-2192	71	3	:	:	PUNCT
ajrhss-2192	71	4	the	the	DET
ajrhss-2192	71	5	exponential	exponential	ADJ
ajrhss-2192	71	6	function	function	NOUN
ajrhss-2192	71	7	is	be	AUX
ajrhss-2192	71	8	extended	extend	VERB
ajrhss-2192	71	9	to	to	ADP
ajrhss-2192	71	10	complex	complex	ADJ
ajrhss-2192	71	11	numbers	number	NOUN
ajrhss-2192	71	12	,	,	PUNCT
ajrhss-2192	71	13	defined	define	VERB
ajrhss-2192	71	14	as	as	ADP
ajrhss-2192	71	15	\	\	PROPN
ajrhss-2192	71	16	(	(	PUNCT
ajrhss-2192	71	17	e^z	e^z	PROPN
ajrhss-2192	71	18	\	\	PROPN
ajrhss-2192	71	19	)	)	PUNCT
ajrhss-2192	71	20	where	where	SCONJ
ajrhss-2192	71	21	\	\	PROPN
ajrhss-2192	71	22	(	(	PUNCT
ajrhss-2192	71	23	z	z	NOUN
ajrhss-2192	71	24	\	\	NOUN
ajrhss-2192	71	25	)	)	PUNCT
ajrhss-2192	71	26	is	be	AUX
ajrhss-2192	71	27	a	a	DET
ajrhss-2192	71	28	complex	complex	ADJ
ajrhss-2192	71	29	number	number	NOUN
ajrhss-2192	71	30	.	.	PUNCT
ajrhss-2192	72	1	euler	euler	PROPN
ajrhss-2192	72	2	's	's	PART
ajrhss-2192	72	3	formula	formula	NOUN
ajrhss-2192	72	4	,	,	PUNCT
ajrhss-2192	72	5	\	\	PROPN
ajrhss-2192	72	6	(	(	PUNCT
ajrhss-2192	72	7	e^{ix	e^{ix	NOUN
ajrhss-2192	72	8	}	}	PUNCT
ajrhss-2192	72	9	=	=	SYM
ajrhss-2192	72	10	\cos(x	\cos(x	PROPN
ajrhss-2192	72	11	)	)	PUNCT
ajrhss-2192	72	12	+	+	CCONJ
ajrhss-2192	72	13	i\sin(x	i\sin(x	X
ajrhss-2192	72	14	)	)	PUNCT
ajrhss-2192	72	15	\	\	NOUN
ajrhss-2192	72	16	)	)	PUNCT
ajrhss-2192	72	17	,	,	PUNCT
ajrhss-2192	72	18	connects	connect	VERB
ajrhss-2192	72	19	exponential	exponential	ADJ
ajrhss-2192	72	20	functions	function	NOUN
ajrhss-2192	72	21	to	to	ADP
ajrhss-2192	72	22	trigonometric	trigonometric	ADJ
ajrhss-2192	72	23	functions	function	NOUN
ajrhss-2192	72	24	and	and	CCONJ
ajrhss-2192	72	25	is	be	AUX
ajrhss-2192	72	26	fundamental	fundamental	ADJ
ajrhss-2192	72	27	in	in	ADP
ajrhss-2192	72	28	the	the	DET
ajrhss-2192	72	29	study	study	NOUN
ajrhss-2192	72	30	of	of	ADP
ajrhss-2192	72	31	complex	complex	ADJ
ajrhss-2192	72	32	numbers	number	NOUN
ajrhss-2192	72	33	and	and	CCONJ
ajrhss-2192	72	34	fourier	fouri	ADJ
ajrhss-2192	72	35	analysis	analysis	NOUN
ajrhss-2192	72	36	.	.	PUNCT
ajrhss-2192	73	1	2	2	X
ajrhss-2192	73	2	.	.	X
ajrhss-2192	73	3	differential	differential	ADJ
ajrhss-2192	73	4	equations	equation	NOUN
ajrhss-2192	73	5	:	:	PUNCT
ajrhss-2192	73	6	solutions	solution	NOUN
ajrhss-2192	73	7	to	to	PART
ajrhss-2192	73	8	linear	linear	VERB
ajrhss-2192	73	9	differential	differential	ADJ
ajrhss-2192	73	10	equations	equation	NOUN
ajrhss-2192	73	11	often	often	ADV
ajrhss-2192	73	12	involve	involve	VERB
ajrhss-2192	73	13	exponential	exponential	ADJ
ajrhss-2192	73	14	functions	function	NOUN
ajrhss-2192	73	15	.	.	PUNCT
ajrhss-2192	74	1	the	the	DET
ajrhss-2192	74	2	characteristic	characteristic	ADJ
ajrhss-2192	74	3	equation	equation	NOUN
ajrhss-2192	74	4	of	of	ADP
ajrhss-2192	74	5	a	a	DET
ajrhss-2192	74	6	linear	linear	ADJ
ajrhss-2192	74	7	differential	differential	ADJ
ajrhss-2192	74	8	equation	equation	NOUN
ajrhss-2192	74	9	with	with	ADP
ajrhss-2192	74	10	constant	constant	ADJ
ajrhss-2192	74	11	coefficients	coefficient	NOUN
ajrhss-2192	74	12	leads	lead	VERB
ajrhss-2192	74	13	to	to	ADP
ajrhss-2192	74	14	solutions	solution	NOUN
ajrhss-2192	74	15	of	of	ADP
ajrhss-2192	74	16	the	the	DET
ajrhss-2192	74	17	form	form	NOUN
ajrhss-2192	74	18	\	\	PROPN
ajrhss-2192	74	19	(	(	PUNCT
ajrhss-2192	74	20	e^{\lambda	e^{\lambda	PROPN
ajrhss-2192	74	21	t	t	PROPN
ajrhss-2192	74	22	}	}	PUNCT
ajrhss-2192	74	23	\	\	PROPN
ajrhss-2192	74	24	)	)	PUNCT
ajrhss-2192	74	25	.	.	PUNCT
ajrhss-2192	75	1	american	american	PROPN
ajrhss-2192	75	2	journal	journal	PROPN
ajrhss-2192	75	3	of	of	ADP
ajrhss-2192	75	4	research	research	NOUN
ajrhss-2192	75	5	in	in	ADP
ajrhss-2192	75	6	humanities	humanity	NOUN
ajrhss-2192	75	7	and	and	CCONJ
ajrhss-2192	75	8	social	social	ADJ
ajrhss-2192	75	9	sciences	science	NOUN
ajrhss-2192	75	10	volume	volume	NOUN
ajrhss-2192	75	11	25	25	NUM
ajrhss-2192	75	12	june	june	PROPN
ajrhss-2192	75	13	2024	2024	NUM
ajrhss-2192	75	14	p	p	NOUN
ajrhss-2192	75	15	a	a	DET
ajrhss-2192	75	16	g	g	NOUN
ajrhss-2192	75	17	e	e	NOUN
ajrhss-2192	76	1	|	|	ADV
ajrhss-2192	76	2	34	34	NUM
ajrhss-2192	76	3	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	76	4	3	3	NUM
ajrhss-2192	76	5	.	.	PUNCT
ajrhss-2192	77	1	linear	linear	PROPN
ajrhss-2192	77	2	algebra	algebra	PROPN
ajrhss-2192	77	3	:	:	PUNCT
ajrhss-2192	77	4	the	the	DET
ajrhss-2192	77	5	matrix	matrix	NOUN
ajrhss-2192	77	6	exponential	exponential	NOUN
ajrhss-2192	77	7	is	be	AUX
ajrhss-2192	77	8	used	use	VERB
ajrhss-2192	77	9	to	to	PART
ajrhss-2192	77	10	solve	solve	VERB
ajrhss-2192	77	11	systems	system	NOUN
ajrhss-2192	77	12	of	of	ADP
ajrhss-2192	77	13	linear	linear	PROPN
ajrhss-2192	77	14	differential	differential	ADJ
ajrhss-2192	77	15	equations	equation	NOUN
ajrhss-2192	77	16	.	.	PUNCT
ajrhss-2192	78	1	it	it	PRON
ajrhss-2192	78	2	plays	play	VERB
ajrhss-2192	78	3	a	a	DET
ajrhss-2192	78	4	role	role	NOUN
ajrhss-2192	78	5	in	in	ADP
ajrhss-2192	78	6	understanding	understand	VERB
ajrhss-2192	78	7	the	the	DET
ajrhss-2192	78	8	behavior	behavior	NOUN
ajrhss-2192	78	9	of	of	ADP
ajrhss-2192	78	10	linear	linear	PROPN
ajrhss-2192	78	11	dynamical	dynamical	ADJ
ajrhss-2192	78	12	systems	system	NOUN
ajrhss-2192	78	13	.	.	PUNCT
ajrhss-2192	79	1	theoretical	theoretical	ADJ
ajrhss-2192	79	2	importance	importance	NOUN
ajrhss-2192	79	3	1	1	NUM
ajrhss-2192	79	4	.	.	PUNCT
ajrhss-2192	80	1	logarithms	logarithm	NOUN
ajrhss-2192	80	2	:	:	PUNCT
ajrhss-2192	80	3	the	the	DET
ajrhss-2192	80	4	natural	natural	ADJ
ajrhss-2192	80	5	logarithm	logarithm	NOUN
ajrhss-2192	80	6	function	function	NOUN
ajrhss-2192	80	7	\	\	PROPN
ajrhss-2192	80	8	(	(	PUNCT
ajrhss-2192	80	9	\ln(x	\ln(x	NUM
ajrhss-2192	80	10	)	)	PUNCT
ajrhss-2192	80	11	\	\	NOUN
ajrhss-2192	80	12	)	)	PUNCT
ajrhss-2192	80	13	is	be	AUX
ajrhss-2192	80	14	the	the	DET
ajrhss-2192	80	15	inverse	inverse	NOUN
ajrhss-2192	80	16	of	of	ADP
ajrhss-2192	80	17	the	the	DET
ajrhss-2192	80	18	natural	natural	ADJ
ajrhss-2192	80	19	exponential	exponential	ADJ
ajrhss-2192	80	20	function	function	NOUN
ajrhss-2192	80	21	\	\	PROPN
ajrhss-2192	80	22	(	(	PUNCT
ajrhss-2192	80	23	e^x	e^x	PROPN
ajrhss-2192	80	24	\	\	PROPN
ajrhss-2192	80	25	)	)	PUNCT
ajrhss-2192	80	26	.	.	PUNCT
ajrhss-2192	81	1	logarithms	logarithm	NOUN
ajrhss-2192	81	2	simplify	simplify	VERB
ajrhss-2192	81	3	the	the	DET
ajrhss-2192	81	4	solving	solving	NOUN
ajrhss-2192	81	5	of	of	ADP
ajrhss-2192	81	6	exponential	exponential	ADJ
ajrhss-2192	81	7	equations	equation	NOUN
ajrhss-2192	81	8	and	and	CCONJ
ajrhss-2192	81	9	are	be	AUX
ajrhss-2192	81	10	used	use	VERB
ajrhss-2192	81	11	extensively	extensively	ADV
ajrhss-2192	81	12	in	in	ADP
ajrhss-2192	81	13	various	various	ADJ
ajrhss-2192	81	14	fields	field	NOUN
ajrhss-2192	81	15	including	include	VERB
ajrhss-2192	81	16	information	information	NOUN
ajrhss-2192	81	17	theory	theory	NOUN
ajrhss-2192	81	18	and	and	CCONJ
ajrhss-2192	81	19	entropy	entropy	NOUN
ajrhss-2192	81	20	calculations	calculation	NOUN
ajrhss-2192	81	21	.	.	PUNCT
ajrhss-2192	82	1	2	2	X
ajrhss-2192	82	2	.	.	X
ajrhss-2192	82	3	series	series	NOUN
ajrhss-2192	82	4	expansion	expansion	NOUN
ajrhss-2192	82	5	:	:	PUNCT
ajrhss-2192	82	6	the	the	DET
ajrhss-2192	82	7	exponential	exponential	ADJ
ajrhss-2192	82	8	function	function	NOUN
ajrhss-2192	82	9	\	\	PROPN
ajrhss-2192	82	10	(	(	PUNCT
ajrhss-2192	82	11	e^x	e^x	PROPN
ajrhss-2192	82	12	\	\	PROPN
ajrhss-2192	82	13	)	)	PUNCT
ajrhss-2192	82	14	can	can	AUX
ajrhss-2192	82	15	be	be	AUX
ajrhss-2192	82	16	expressed	express	VERB
ajrhss-2192	82	17	as	as	ADP
ajrhss-2192	82	18	an	an	DET
ajrhss-2192	82	19	infinite	infinite	ADJ
ajrhss-2192	82	20	series	series	NOUN
ajrhss-2192	82	21	:	:	PUNCT
ajrhss-2192	82	22	\	\	PROPN
ajrhss-2192	82	23	[	[	PUNCT
ajrhss-2192	82	24	e^x	e^x	NOUN
ajrhss-2192	82	25	=	=	PROPN
ajrhss-2192	82	26	\sum_{n=0}^{\infty	\sum_{n=0}^{\infty	PROPN
ajrhss-2192	82	27	}	}	PUNCT
ajrhss-2192	82	28	\frac{x^n}{n	\frac{x^n}{n	NOUN
ajrhss-2192	82	29	!	!	PUNCT
ajrhss-2192	82	30	}	}	PUNCT
ajrhss-2192	83	1	\	\	NOUN
ajrhss-2192	83	2	]	]	PUNCT
ajrhss-2192	83	3	this	this	DET
ajrhss-2192	83	4	series	series	NOUN
ajrhss-2192	83	5	expansion	expansion	NOUN
ajrhss-2192	83	6	is	be	AUX
ajrhss-2192	83	7	foundational	foundational	ADJ
ajrhss-2192	83	8	in	in	ADP
ajrhss-2192	83	9	analysis	analysis	NOUN
ajrhss-2192	83	10	and	and	CCONJ
ajrhss-2192	83	11	used	use	VERB
ajrhss-2192	83	12	in	in	ADP
ajrhss-2192	83	13	solving	solve	VERB
ajrhss-2192	83	14	differential	differential	ADJ
ajrhss-2192	83	15	equations	equation	NOUN
ajrhss-2192	83	16	and	and	CCONJ
ajrhss-2192	83	17	approximating	approximate	VERB
ajrhss-2192	83	18	functions	function	NOUN
ajrhss-2192	83	19	.	.	PUNCT
ajrhss-2192	84	1	exponential	exponential	ADJ
ajrhss-2192	84	2	growth	growth	NOUN
ajrhss-2192	84	3	and	and	CCONJ
ajrhss-2192	84	4	decay	decay	NOUN
ajrhss-2192	84	5	in	in	ADP
ajrhss-2192	84	6	real	real	ADJ
ajrhss-2192	84	7	-	-	PUNCT
ajrhss-2192	84	8	world	world	NOUN
ajrhss-2192	84	9	scenarios	scenario	NOUN
ajrhss-2192	84	10	population	population	NOUN
ajrhss-2192	84	11	growth	growth	NOUN
ajrhss-2192	84	12	:	:	PUNCT
ajrhss-2192	84	13	exponential	exponential	NOUN
ajrhss-2192	84	14	models	model	NOUN
ajrhss-2192	84	15	describe	describe	VERB
ajrhss-2192	84	16	how	how	SCONJ
ajrhss-2192	84	17	populations	population	NOUN
ajrhss-2192	84	18	grow	grow	VERB
ajrhss-2192	84	19	rapidly	rapidly	ADV
ajrhss-2192	84	20	under	under	ADP
ajrhss-2192	84	21	ideal	ideal	ADJ
ajrhss-2192	84	22	conditions	condition	NOUN
ajrhss-2192	84	23	before	before	ADP
ajrhss-2192	84	24	leveling	level	VERB
ajrhss-2192	84	25	off	off	ADP
ajrhss-2192	84	26	as	as	SCONJ
ajrhss-2192	84	27	resources	resource	NOUN
ajrhss-2192	84	28	become	become	VERB
ajrhss-2192	84	29	limited	limited	ADJ
ajrhss-2192	84	30	.	.	PUNCT
ajrhss-2192	85	1	radioactive	radioactive	ADJ
ajrhss-2192	85	2	decay	decay	NOUN
ajrhss-2192	85	3	:	:	PUNCT
ajrhss-2192	85	4	the	the	DET
ajrhss-2192	85	5	decay	decay	NOUN
ajrhss-2192	85	6	of	of	ADP
ajrhss-2192	85	7	radioactive	radioactive	ADJ
ajrhss-2192	85	8	substances	substance	NOUN
ajrhss-2192	85	9	follows	follow	VERB
ajrhss-2192	85	10	an	an	DET
ajrhss-2192	85	11	exponential	exponential	ADJ
ajrhss-2192	85	12	law	law	NOUN
ajrhss-2192	85	13	,	,	PUNCT
ajrhss-2192	85	14	crucial	crucial	ADJ
ajrhss-2192	85	15	for	for	ADP
ajrhss-2192	85	16	dating	date	VERB
ajrhss-2192	85	17	archaeological	archaeological	ADJ
ajrhss-2192	85	18	finds	find	NOUN
ajrhss-2192	85	19	and	and	CCONJ
ajrhss-2192	85	20	understanding	understand	VERB
ajrhss-2192	85	21	nuclear	nuclear	ADJ
ajrhss-2192	85	22	processes	process	NOUN
ajrhss-2192	85	23	.	.	PUNCT
ajrhss-2192	86	1	financial	financial	ADJ
ajrhss-2192	86	2	modeling	modeling	NOUN
ajrhss-2192	86	3	:	:	PUNCT
ajrhss-2192	86	4	exponential	exponential	ADJ
ajrhss-2192	86	5	functions	function	NOUN
ajrhss-2192	86	6	model	model	VERB
ajrhss-2192	86	7	how	how	SCONJ
ajrhss-2192	86	8	investments	investment	NOUN
ajrhss-2192	86	9	grow	grow	VERB
ajrhss-2192	86	10	over	over	ADP
ajrhss-2192	86	11	time	time	NOUN
ajrhss-2192	86	12	with	with	ADP
ajrhss-2192	86	13	compound	compound	NOUN
ajrhss-2192	86	14	interest	interest	NOUN
ajrhss-2192	86	15	,	,	PUNCT
ajrhss-2192	86	16	essential	essential	ADJ
ajrhss-2192	86	17	in	in	ADP
ajrhss-2192	86	18	personal	personal	ADJ
ajrhss-2192	86	19	finance	finance	NOUN
ajrhss-2192	86	20	and	and	CCONJ
ajrhss-2192	86	21	actuarial	actuarial	ADJ
ajrhss-2192	86	22	science	science	NOUN
ajrhss-2192	86	23	.	.	PUNCT
ajrhss-2192	87	1	let	let	VERB
ajrhss-2192	87	2	's	us	PRON
ajrhss-2192	87	3	delve	delve	VERB
ajrhss-2192	87	4	deeper	deep	ADJ
ajrhss-2192	87	5	into	into	ADP
ajrhss-2192	87	6	the	the	DET
ajrhss-2192	87	7	role	role	NOUN
ajrhss-2192	87	8	of	of	ADP
ajrhss-2192	87	9	exponential	exponential	ADJ
ajrhss-2192	87	10	functions	function	NOUN
ajrhss-2192	87	11	in	in	ADP
ajrhss-2192	87	12	mathematics	mathematic	NOUN
ajrhss-2192	87	13	,	,	PUNCT
ajrhss-2192	87	14	highlighting	highlight	VERB
ajrhss-2192	87	15	their	their	PRON
ajrhss-2192	87	16	properties	property	NOUN
ajrhss-2192	87	17	,	,	PUNCT
ajrhss-2192	87	18	applications	application	NOUN
ajrhss-2192	87	19	,	,	PUNCT
ajrhss-2192	87	20	and	and	CCONJ
ajrhss-2192	87	21	significance	significance	NOUN
ajrhss-2192	87	22	in	in	ADP
ajrhss-2192	87	23	various	various	ADJ
ajrhss-2192	87	24	fields	field	NOUN
ajrhss-2192	87	25	.	.	PUNCT
ajrhss-2192	88	1	detailed	detailed	ADJ
ajrhss-2192	88	2	properties	property	NOUN
ajrhss-2192	88	3	of	of	ADP
ajrhss-2192	88	4	exponential	exponential	ADJ
ajrhss-2192	88	5	functions	function	NOUN
ajrhss-2192	88	6	1	1	NUM
ajrhss-2192	88	7	.	.	PUNCT
ajrhss-2192	88	8	exponent	exponent	NOUN
ajrhss-2192	88	9	laws	law	NOUN
ajrhss-2192	88	10	:	:	PUNCT
ajrhss-2192	88	11	exponential	exponential	NOUN
ajrhss-2192	88	12	functions	function	NOUN
ajrhss-2192	88	13	follow	follow	VERB
ajrhss-2192	88	14	specific	specific	ADJ
ajrhss-2192	88	15	rules	rule	NOUN
ajrhss-2192	88	16	that	that	PRON
ajrhss-2192	88	17	simplify	simplify	VERB
ajrhss-2192	88	18	their	their	PRON
ajrhss-2192	88	19	manipulation	manipulation	NOUN
ajrhss-2192	88	20	:	:	PUNCT
ajrhss-2192	89	1	\	\	PROPN
ajrhss-2192	89	2	[	[	PUNCT
ajrhss-2192	89	3	b^{x+y	b^{x+y	NOUN
ajrhss-2192	89	4	}	}	PUNCT
ajrhss-2192	89	5	=	=	SYM
ajrhss-2192	89	6	b^x	b^x	ADJ
ajrhss-2192	89	7	\cdot	\cdot	NOUN
ajrhss-2192	89	8	b^y	b^y	NOUN
ajrhss-2192	89	9	\	\	PROPN
ajrhss-2192	89	10	]	]	PUNCT
ajrhss-2192	89	11	\	\	PROPN
ajrhss-2192	89	12	[	[	PUNCT
ajrhss-2192	89	13	\left	\left	PROPN
ajrhss-2192	89	14	(	(	PUNCT
ajrhss-2192	89	15	b^x	b^x	ADJ
ajrhss-2192	89	16	\right)^y	\right)^y	PROPN
ajrhss-2192	89	17	=	=	SYM
ajrhss-2192	89	18	b^{xy	b^{xy	PROPN
ajrhss-2192	89	19	}	}	PUNCT
ajrhss-2192	89	20	\	\	NOUN
ajrhss-2192	89	21	]	]	PUNCT
ajrhss-2192	89	22	\	\	PROPN
ajrhss-2192	89	23	[	[	PUNCT
ajrhss-2192	89	24	b^{-x	b^{-x	X
ajrhss-2192	89	25	}	}	PUNCT
ajrhss-2192	89	26	=	=	SYM
ajrhss-2192	89	27	\frac{1}{b^x	\frac{1}{b^x	ADJ
ajrhss-2192	89	28	}	}	PUNCT
ajrhss-2192	89	29	\	\	NOUN
ajrhss-2192	89	30	]	]	PUNCT
ajrhss-2192	89	31	\	\	ADJ
ajrhss-2192	89	32	[	[	PUNCT
ajrhss-2192	89	33	b^0	b^0	NOUN
ajrhss-2192	89	34	=	=	SYM
ajrhss-2192	89	35	1	1	NUM
ajrhss-2192	89	36	\	\	NOUN
ajrhss-2192	89	37	]	]	PUNCT
ajrhss-2192	89	38	2	2	X
ajrhss-2192	89	39	.	.	PUNCT
ajrhss-2192	89	40	inverse	inverse	NOUN
ajrhss-2192	89	41	relationship	relationship	NOUN
ajrhss-2192	89	42	with	with	ADP
ajrhss-2192	89	43	logarithms	logarithm	NOUN
ajrhss-2192	89	44	:	:	PUNCT
ajrhss-2192	89	45	the	the	DET
ajrhss-2192	89	46	exponential	exponential	ADJ
ajrhss-2192	89	47	function	function	NOUN
ajrhss-2192	89	48	\	\	PROPN
ajrhss-2192	89	49	(	(	PUNCT
ajrhss-2192	89	50	b^x	b^x	PROPN
ajrhss-2192	89	51	\	\	PROPN
ajrhss-2192	89	52	)	)	PUNCT
ajrhss-2192	89	53	is	be	AUX
ajrhss-2192	89	54	the	the	DET
ajrhss-2192	89	55	inverse	inverse	NOUN
ajrhss-2192	89	56	of	of	ADP
ajrhss-2192	89	57	the	the	DET
ajrhss-2192	89	58	logarithmic	logarithmic	ADJ
ajrhss-2192	89	59	function	function	NOUN
ajrhss-2192	89	60	\	\	PROPN
ajrhss-2192	89	61	(	(	PUNCT
ajrhss-2192	89	62	\log_b(x	\log_b(x	ADJ
ajrhss-2192	89	63	)	)	PUNCT
ajrhss-2192	89	64	\	\	NOUN
ajrhss-2192	89	65	)	)	PUNCT
ajrhss-2192	89	66	.	.	PUNCT
ajrhss-2192	90	1	this	this	DET
ajrhss-2192	90	2	relationship	relationship	NOUN
ajrhss-2192	90	3	is	be	AUX
ajrhss-2192	90	4	fundamental	fundamental	ADJ
ajrhss-2192	90	5	in	in	ADP
ajrhss-2192	90	6	solving	solve	VERB
ajrhss-2192	90	7	equations	equation	NOUN
ajrhss-2192	90	8	involving	involve	VERB
ajrhss-2192	90	9	exponentials	exponential	NOUN
ajrhss-2192	90	10	and	and	CCONJ
ajrhss-2192	90	11	logarithms	logarithm	NOUN
ajrhss-2192	90	12	.	.	PUNCT
ajrhss-2192	91	1	\	\	NOUN
ajrhss-2192	91	2	[	[	PUNCT
ajrhss-2192	91	3	b^x	b^x	PROPN
ajrhss-2192	91	4	=	=	SYM
ajrhss-2192	91	5	y	y	PROPN
ajrhss-2192	91	6	\implies	\implie	NOUN
ajrhss-2192	91	7	x	x	PUNCT
ajrhss-2192	91	8	=	=	SYM
ajrhss-2192	91	9	\log_b(y	\log_b(y	ADJ
ajrhss-2192	91	10	)	)	PUNCT
ajrhss-2192	92	1	\	\	NOUN
ajrhss-2192	92	2	]	]	X
ajrhss-2192	92	3	3	3	X
ajrhss-2192	92	4	.	.	X
ajrhss-2192	92	5	behavior	behavior	NOUN
ajrhss-2192	92	6	and	and	CCONJ
ajrhss-2192	92	7	limits	limit	NOUN
ajrhss-2192	92	8	:	:	PUNCT
ajrhss-2192	92	9	as	as	ADP
ajrhss-2192	92	10	\	\	PROPN
ajrhss-2192	92	11	(	(	PUNCT
ajrhss-2192	92	12	x	x	PROPN
ajrhss-2192	92	13	\to	\to	PROPN
ajrhss-2192	92	14	\infty	\infty	PROPN
ajrhss-2192	92	15	\	\	PROPN
ajrhss-2192	92	16	)	)	PUNCT
ajrhss-2192	92	17	,	,	PUNCT
ajrhss-2192	92	18	\	\	PROPN
ajrhss-2192	92	19	(	(	PUNCT
ajrhss-2192	92	20	b^x	b^x	ADJ
ajrhss-2192	92	21	\to	\to	PROPN
ajrhss-2192	92	22	\infty	\infty	PROPN
ajrhss-2192	92	23	\	\	NOUN
ajrhss-2192	92	24	)	)	PUNCT
ajrhss-2192	92	25	if	if	SCONJ
ajrhss-2192	92	26	\	\	PROPN
ajrhss-2192	92	27	(	(	PUNCT
ajrhss-2192	92	28	b	b	X
ajrhss-2192	92	29	>	>	SYM
ajrhss-2192	92	30	1	1	NUM
ajrhss-2192	92	31	\	\	NOUN
ajrhss-2192	92	32	)	)	PUNCT
ajrhss-2192	92	33	and	and	CCONJ
ajrhss-2192	92	34	\	\	PROPN
ajrhss-2192	92	35	(	(	PUNCT
ajrhss-2192	92	36	b^x	b^x	ADJ
ajrhss-2192	92	37	\to	\to	PROPN
ajrhss-2192	92	38	0	0	NUM
ajrhss-2192	92	39	\	\	NOUN
ajrhss-2192	92	40	)	)	PUNCT
ajrhss-2192	92	41	if	if	SCONJ
ajrhss-2192	92	42	\	\	PROPN
ajrhss-2192	92	43	(	(	PUNCT
ajrhss-2192	92	44	0	0	NUM
ajrhss-2192	92	45	<	<	X
ajrhss-2192	92	46	b	b	X
ajrhss-2192	92	47	<	<	X
ajrhss-2192	92	48	1	1	NUM
ajrhss-2192	92	49	\	\	NOUN
ajrhss-2192	92	50	)	)	PUNCT
ajrhss-2192	92	51	.	.	PUNCT
ajrhss-2192	93	1	as	as	ADP
ajrhss-2192	93	2	\	\	PROPN
ajrhss-2192	93	3	(	(	PUNCT
ajrhss-2192	93	4	x	x	PROPN
ajrhss-2192	93	5	\to	\to	PROPN
ajrhss-2192	93	6	-\infty	-\infty	PROPN
ajrhss-2192	93	7	\	\	PROPN
ajrhss-2192	93	8	)	)	PUNCT
ajrhss-2192	93	9	,	,	PUNCT
ajrhss-2192	93	10	\	\	PROPN
ajrhss-2192	93	11	(	(	PUNCT
ajrhss-2192	93	12	b^x	b^x	ADJ
ajrhss-2192	93	13	\to	\to	PROPN
ajrhss-2192	93	14	0	0	NUM
ajrhss-2192	93	15	\	\	NOUN
ajrhss-2192	93	16	)	)	PUNCT
ajrhss-2192	93	17	for	for	ADP
ajrhss-2192	93	18	\	\	PROPN
ajrhss-2192	93	19	(	(	PUNCT
ajrhss-2192	93	20	b	b	X
ajrhss-2192	93	21	>	>	SYM
ajrhss-2192	93	22	1	1	NUM
ajrhss-2192	93	23	\	\	NOUN
ajrhss-2192	93	24	)	)	PUNCT
ajrhss-2192	93	25	.	.	PUNCT
ajrhss-2192	94	1	american	american	PROPN
ajrhss-2192	94	2	journal	journal	PROPN
ajrhss-2192	94	3	of	of	ADP
ajrhss-2192	94	4	research	research	NOUN
ajrhss-2192	94	5	in	in	ADP
ajrhss-2192	94	6	humanities	humanity	NOUN
ajrhss-2192	94	7	and	and	CCONJ
ajrhss-2192	94	8	social	social	ADJ
ajrhss-2192	94	9	sciences	science	NOUN
ajrhss-2192	94	10	volume	volume	NOUN
ajrhss-2192	94	11	25	25	NUM
ajrhss-2192	94	12	june	june	PROPN
ajrhss-2192	94	13	2024	2024	NUM
ajrhss-2192	94	14	p	p	NOUN
ajrhss-2192	94	15	a	a	DET
ajrhss-2192	94	16	g	g	NOUN
ajrhss-2192	94	17	e	e	NOUN
ajrhss-2192	94	18	|	|	ADV
ajrhss-2192	94	19	35	35	NUM
ajrhss-2192	94	20	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	94	21	applications	application	NOUN
ajrhss-2192	94	22	in	in	ADP
ajrhss-2192	94	23	various	various	ADJ
ajrhss-2192	94	24	fields	field	NOUN
ajrhss-2192	94	25	mathematics	mathematic	NOUN
ajrhss-2192	94	26	1	1	NUM
ajrhss-2192	94	27	.	.	PUNCT
ajrhss-2192	94	28	calculus	calculus	NOUN
ajrhss-2192	94	29	:	:	PUNCT
ajrhss-2192	94	30	exponential	exponential	ADJ
ajrhss-2192	94	31	functions	function	NOUN
ajrhss-2192	94	32	are	be	AUX
ajrhss-2192	94	33	pivotal	pivotal	ADJ
ajrhss-2192	94	34	in	in	ADP
ajrhss-2192	94	35	calculus	calculus	NOUN
ajrhss-2192	94	36	,	,	PUNCT
ajrhss-2192	94	37	particularly	particularly	ADV
ajrhss-2192	94	38	in	in	ADP
ajrhss-2192	94	39	solving	solve	VERB
ajrhss-2192	94	40	differential	differential	NOUN
ajrhss-2192	94	41	equations	equation	NOUN
ajrhss-2192	94	42	.	.	PUNCT
ajrhss-2192	95	1	they	they	PRON
ajrhss-2192	95	2	simplify	simplify	VERB
ajrhss-2192	95	3	the	the	DET
ajrhss-2192	95	4	calculation	calculation	NOUN
ajrhss-2192	95	5	of	of	ADP
ajrhss-2192	95	6	limits	limit	NOUN
ajrhss-2192	95	7	,	,	PUNCT
ajrhss-2192	95	8	especially	especially	ADV
ajrhss-2192	95	9	in	in	ADP
ajrhss-2192	95	10	indeterminate	indeterminate	ADJ
ajrhss-2192	95	11	forms	form	NOUN
ajrhss-2192	95	12	involving	involve	VERB
ajrhss-2192	95	13	growth	growth	NOUN
ajrhss-2192	95	14	rates	rate	NOUN
ajrhss-2192	95	15	.	.	PUNCT
ajrhss-2192	96	1	2	2	X
ajrhss-2192	96	2	.	.	X
ajrhss-2192	96	3	complex	complex	ADJ
ajrhss-2192	96	4	analysis	analysis	NOUN
ajrhss-2192	96	5	:	:	PUNCT
ajrhss-2192	96	6	the	the	DET
ajrhss-2192	96	7	function	function	NOUN
ajrhss-2192	96	8	\	\	PROPN
ajrhss-2192	96	9	(	(	PUNCT
ajrhss-2192	96	10	e^z	e^z	PROPN
ajrhss-2192	96	11	\	\	PROPN
ajrhss-2192	96	12	)	)	PUNCT
ajrhss-2192	96	13	,	,	PUNCT
ajrhss-2192	96	14	where	where	SCONJ
ajrhss-2192	96	15	\	\	PROPN
ajrhss-2192	96	16	(	(	PUNCT
ajrhss-2192	96	17	z	z	NOUN
ajrhss-2192	96	18	\	\	NOUN
ajrhss-2192	96	19	)	)	PUNCT
ajrhss-2192	96	20	is	be	AUX
ajrhss-2192	96	21	a	a	DET
ajrhss-2192	96	22	complex	complex	ADJ
ajrhss-2192	96	23	number	number	NOUN
ajrhss-2192	96	24	,	,	PUNCT
ajrhss-2192	96	25	has	have	VERB
ajrhss-2192	96	26	significant	significant	ADJ
ajrhss-2192	96	27	applications	application	NOUN
ajrhss-2192	96	28	in	in	ADP
ajrhss-2192	96	29	complex	complex	ADJ
ajrhss-2192	96	30	analysis	analysis	NOUN
ajrhss-2192	96	31	.	.	PUNCT
ajrhss-2192	96	32	euler	euler	PROPN
ajrhss-2192	96	33	's	's	PART
ajrhss-2192	96	34	formula	formula	NOUN
ajrhss-2192	96	35	,	,	PUNCT
ajrhss-2192	96	36	\	\	PROPN
ajrhss-2192	96	37	(	(	PUNCT
ajrhss-2192	96	38	e^{ix	e^{ix	NOUN
ajrhss-2192	96	39	}	}	PUNCT
ajrhss-2192	96	40	=	=	SYM
ajrhss-2192	96	41	\cos(x	\cos(x	PROPN
ajrhss-2192	96	42	)	)	PUNCT
ajrhss-2192	96	43	+	+	CCONJ
ajrhss-2192	96	44	i\sin(x	i\sin(x	X
ajrhss-2192	96	45	)	)	PUNCT
ajrhss-2192	96	46	\	\	NOUN
ajrhss-2192	96	47	)	)	PUNCT
ajrhss-2192	96	48	,	,	PUNCT
ajrhss-2192	96	49	bridges	bridge	NOUN
ajrhss-2192	96	50	trigonometric	trigonometric	ADJ
ajrhss-2192	96	51	and	and	CCONJ
ajrhss-2192	96	52	exponential	exponential	ADJ
ajrhss-2192	96	53	functions	function	NOUN
ajrhss-2192	96	54	.	.	PUNCT
ajrhss-2192	97	1	3	3	X
ajrhss-2192	97	2	.	.	X
ajrhss-2192	97	3	series	series	NOUN
ajrhss-2192	97	4	and	and	CCONJ
ajrhss-2192	97	5	sequences	sequence	NOUN
ajrhss-2192	97	6	:	:	PUNCT
ajrhss-2192	97	7	the	the	DET
ajrhss-2192	97	8	taylor	taylor	PROPN
ajrhss-2192	97	9	series	series	PROPN
ajrhss-2192	97	10	expansion	expansion	NOUN
ajrhss-2192	97	11	of	of	ADP
ajrhss-2192	97	12	\	\	PROPN
ajrhss-2192	97	13	(	(	PUNCT
ajrhss-2192	97	14	e^x	e^x	PROPN
ajrhss-2192	97	15	\	\	PROPN
ajrhss-2192	97	16	)	)	PUNCT
ajrhss-2192	97	17	is	be	AUX
ajrhss-2192	97	18	crucial	crucial	ADJ
ajrhss-2192	97	19	for	for	ADP
ajrhss-2192	97	20	approximations	approximation	NOUN
ajrhss-2192	97	21	:	:	PUNCT
ajrhss-2192	97	22	\	\	PROPN
ajrhss-2192	97	23	[	[	PUNCT
ajrhss-2192	97	24	e^x	e^x	NOUN
ajrhss-2192	97	25	=	=	PROPN
ajrhss-2192	97	26	\sum_{n=0}^{\infty	\sum_{n=0}^{\infty	PROPN
ajrhss-2192	97	27	}	}	PUNCT
ajrhss-2192	97	28	\frac{x^n}{n	\frac{x^n}{n	NOUN
ajrhss-2192	97	29	!	!	PUNCT
ajrhss-2192	97	30	}	}	PUNCT
ajrhss-2192	98	1	\	\	NOUN
ajrhss-2192	98	2	]	]	PUNCT
ajrhss-2192	98	3	this	this	DET
ajrhss-2192	98	4	series	series	NOUN
ajrhss-2192	98	5	is	be	AUX
ajrhss-2192	98	6	used	use	VERB
ajrhss-2192	98	7	in	in	ADP
ajrhss-2192	98	8	various	various	ADJ
ajrhss-2192	98	9	mathematical	mathematical	ADJ
ajrhss-2192	98	10	and	and	CCONJ
ajrhss-2192	98	11	engineering	engineering	NOUN
ajrhss-2192	98	12	applications	application	NOUN
ajrhss-2192	98	13	to	to	ADP
ajrhss-2192	98	14	approximate	approximate	ADJ
ajrhss-2192	98	15	functions	function	NOUN
ajrhss-2192	98	16	.	.	PUNCT
ajrhss-2192	99	1	physics	physics	NOUN
ajrhss-2192	99	2	1	1	NUM
ajrhss-2192	99	3	.	.	PUNCT
ajrhss-2192	99	4	radioactive	radioactive	ADJ
ajrhss-2192	99	5	decay	decay	NOUN
ajrhss-2192	99	6	:	:	PUNCT
ajrhss-2192	99	7	the	the	DET
ajrhss-2192	99	8	quantity	quantity	NOUN
ajrhss-2192	99	9	of	of	ADP
ajrhss-2192	99	10	a	a	DET
ajrhss-2192	99	11	radioactive	radioactive	ADJ
ajrhss-2192	99	12	substance	substance	NOUN
ajrhss-2192	99	13	decreases	decrease	VERB
ajrhss-2192	99	14	exponentially	exponentially	ADV
ajrhss-2192	99	15	over	over	ADP
ajrhss-2192	99	16	time	time	NOUN
ajrhss-2192	99	17	,	,	PUNCT
ajrhss-2192	99	18	described	describe	VERB
ajrhss-2192	99	19	by	by	ADP
ajrhss-2192	99	20	\	\	PROPN
ajrhss-2192	99	21	(	(	PUNCT
ajrhss-2192	99	22	n(t	n(t	PROPN
ajrhss-2192	99	23	)	)	PUNCT
ajrhss-2192	99	24	=	=	PUNCT
ajrhss-2192	100	1	n_0	n_0	NOUN
ajrhss-2192	100	2	e^{-\lambda	e^{-\lambda	PROPN
ajrhss-2192	100	3	t	t	PROPN
ajrhss-2192	100	4	}	}	PUNCT
ajrhss-2192	100	5	\	\	PROPN
ajrhss-2192	100	6	)	)	PUNCT
ajrhss-2192	100	7	,	,	PUNCT
ajrhss-2192	100	8	where	where	SCONJ
ajrhss-2192	100	9	\	\	PROPN
ajrhss-2192	100	10	(	(	PUNCT
ajrhss-2192	100	11	\lambda	\lambda	PROPN
ajrhss-2192	100	12	\	\	PROPN
ajrhss-2192	100	13	)	)	PUNCT
ajrhss-2192	100	14	is	be	AUX
ajrhss-2192	100	15	the	the	DET
ajrhss-2192	100	16	decay	decay	NOUN
ajrhss-2192	100	17	constant	constant	ADJ
ajrhss-2192	100	18	.	.	PUNCT
ajrhss-2192	101	1	2	2	X
ajrhss-2192	101	2	.	.	X
ajrhss-2192	101	3	newton	newton	PROPN
ajrhss-2192	101	4	's	's	PART
ajrhss-2192	101	5	law	law	NOUN
ajrhss-2192	101	6	of	of	ADP
ajrhss-2192	101	7	cooling	cool	VERB
ajrhss-2192	101	8	:	:	PUNCT
ajrhss-2192	101	9	the	the	DET
ajrhss-2192	101	10	temperature	temperature	NOUN
ajrhss-2192	101	11	of	of	ADP
ajrhss-2192	101	12	an	an	DET
ajrhss-2192	101	13	object	object	NOUN
ajrhss-2192	101	14	changes	change	NOUN
ajrhss-2192	101	15	exponentially	exponentially	ADV
ajrhss-2192	101	16	over	over	ADP
ajrhss-2192	101	17	time	time	NOUN
ajrhss-2192	101	18	,	,	PUNCT
ajrhss-2192	101	19	approaching	approach	VERB
ajrhss-2192	101	20	the	the	DET
ajrhss-2192	101	21	ambient	ambient	ADJ
ajrhss-2192	101	22	temperature	temperature	NOUN
ajrhss-2192	101	23	.	.	PUNCT
ajrhss-2192	102	1	3	3	X
ajrhss-2192	102	2	.	.	X
ajrhss-2192	102	3	electrical	electrical	ADJ
ajrhss-2192	102	4	circuits	circuit	NOUN
ajrhss-2192	102	5	:	:	PUNCT
ajrhss-2192	102	6	the	the	DET
ajrhss-2192	102	7	charging	charging	NOUN
ajrhss-2192	102	8	and	and	CCONJ
ajrhss-2192	102	9	discharging	discharge	VERB
ajrhss-2192	102	10	of	of	ADP
ajrhss-2192	102	11	a	a	DET
ajrhss-2192	102	12	capacitor	capacitor	NOUN
ajrhss-2192	102	13	in	in	ADP
ajrhss-2192	102	14	an	an	DET
ajrhss-2192	102	15	rc	rc	PROPN
ajrhss-2192	102	16	circuit	circuit	NOUN
ajrhss-2192	102	17	are	be	AUX
ajrhss-2192	102	18	modeled	model	VERB
ajrhss-2192	102	19	by	by	ADP
ajrhss-2192	102	20	exponential	exponential	ADJ
ajrhss-2192	102	21	functions	function	NOUN
ajrhss-2192	102	22	.	.	PUNCT
ajrhss-2192	103	1	biology	biology	NOUN
ajrhss-2192	103	2	1	1	NUM
ajrhss-2192	103	3	.	.	PUNCT
ajrhss-2192	104	1	population	population	NOUN
ajrhss-2192	104	2	dynamics	dynamic	NOUN
ajrhss-2192	104	3	:	:	PUNCT
ajrhss-2192	104	4	exponential	exponential	NOUN
ajrhss-2192	104	5	models	model	NOUN
ajrhss-2192	104	6	describe	describe	VERB
ajrhss-2192	104	7	the	the	DET
ajrhss-2192	104	8	growth	growth	NOUN
ajrhss-2192	104	9	of	of	ADP
ajrhss-2192	104	10	populations	population	NOUN
ajrhss-2192	104	11	under	under	ADP
ajrhss-2192	104	12	ideal	ideal	ADJ
ajrhss-2192	104	13	conditions	condition	NOUN
ajrhss-2192	104	14	,	,	PUNCT
ajrhss-2192	104	15	where	where	SCONJ
ajrhss-2192	104	16	resources	resource	NOUN
ajrhss-2192	104	17	are	be	AUX
ajrhss-2192	104	18	unlimited	unlimited	ADJ
ajrhss-2192	104	19	.	.	PUNCT
ajrhss-2192	105	1	logistic	logistic	ADJ
ajrhss-2192	105	2	growth	growth	NOUN
ajrhss-2192	105	3	models	model	NOUN
ajrhss-2192	105	4	,	,	PUNCT
ajrhss-2192	105	5	which	which	PRON
ajrhss-2192	105	6	account	account	VERB
ajrhss-2192	105	7	for	for	ADP
ajrhss-2192	105	8	limited	limited	ADJ
ajrhss-2192	105	9	resources	resource	NOUN
ajrhss-2192	105	10	,	,	PUNCT
ajrhss-2192	105	11	start	start	VERB
ajrhss-2192	105	12	with	with	ADP
ajrhss-2192	105	13	an	an	DET
ajrhss-2192	105	14	exponential	exponential	ADJ
ajrhss-2192	105	15	growth	growth	NOUN
ajrhss-2192	105	16	phase	phase	NOUN
ajrhss-2192	105	17	before	before	ADP
ajrhss-2192	105	18	leveling	level	VERB
ajrhss-2192	105	19	off	off	ADP
ajrhss-2192	105	20	.	.	PUNCT
ajrhss-2192	106	1	2	2	X
ajrhss-2192	106	2	.	.	X
ajrhss-2192	106	3	epidemiology	epidemiology	NOUN
ajrhss-2192	106	4	:	:	PUNCT
ajrhss-2192	106	5	the	the	DET
ajrhss-2192	106	6	spread	spread	NOUN
ajrhss-2192	106	7	of	of	ADP
ajrhss-2192	106	8	diseases	disease	NOUN
ajrhss-2192	106	9	can	can	AUX
ajrhss-2192	106	10	initially	initially	ADV
ajrhss-2192	106	11	follow	follow	VERB
ajrhss-2192	106	12	an	an	DET
ajrhss-2192	106	13	exponential	exponential	ADJ
ajrhss-2192	106	14	growth	growth	NOUN
ajrhss-2192	106	15	pattern	pattern	NOUN
ajrhss-2192	106	16	,	,	PUNCT
ajrhss-2192	106	17	particularly	particularly	ADV
ajrhss-2192	106	18	in	in	ADP
ajrhss-2192	106	19	the	the	DET
ajrhss-2192	106	20	early	early	ADJ
ajrhss-2192	106	21	stages	stage	NOUN
ajrhss-2192	106	22	of	of	ADP
ajrhss-2192	106	23	an	an	DET
ajrhss-2192	106	24	outbreak	outbreak	NOUN
ajrhss-2192	106	25	.	.	PUNCT
ajrhss-2192	107	1	american	american	PROPN
ajrhss-2192	107	2	journal	journal	PROPN
ajrhss-2192	107	3	of	of	ADP
ajrhss-2192	107	4	research	research	NOUN
ajrhss-2192	107	5	in	in	ADP
ajrhss-2192	107	6	humanities	humanity	NOUN
ajrhss-2192	107	7	and	and	CCONJ
ajrhss-2192	107	8	social	social	ADJ
ajrhss-2192	107	9	sciences	science	NOUN
ajrhss-2192	107	10	volume	volume	NOUN
ajrhss-2192	107	11	25	25	NUM
ajrhss-2192	107	12	june	june	PROPN
ajrhss-2192	107	13	2024	2024	NUM
ajrhss-2192	107	14	p	p	NOUN
ajrhss-2192	107	15	a	a	DET
ajrhss-2192	107	16	g	g	NOUN
ajrhss-2192	107	17	e	e	NOUN
ajrhss-2192	107	18	|	|	ADV
ajrhss-2192	107	19	36	36	NUM
ajrhss-2192	107	20	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	107	21	finance	finance	NOUN
ajrhss-2192	107	22	1	1	NUM
ajrhss-2192	107	23	.	.	PUNCT
ajrhss-2192	108	1	compound	compound	NOUN
ajrhss-2192	108	2	interest	interest	NOUN
ajrhss-2192	108	3	:	:	PUNCT
ajrhss-2192	108	4	exponential	exponential	NOUN
ajrhss-2192	108	5	functions	function	NOUN
ajrhss-2192	108	6	model	model	VERB
ajrhss-2192	108	7	the	the	DET
ajrhss-2192	108	8	growth	growth	NOUN
ajrhss-2192	108	9	of	of	ADP
ajrhss-2192	108	10	investments	investment	NOUN
ajrhss-2192	108	11	with	with	ADP
ajrhss-2192	108	12	compound	compound	NOUN
ajrhss-2192	108	13	interest	interest	NOUN
ajrhss-2192	108	14	,	,	PUNCT
ajrhss-2192	108	15	using	use	VERB
ajrhss-2192	108	16	the	the	DET
ajrhss-2192	108	17	formula	formula	NOUN
ajrhss-2192	108	18	\	\	PROPN
ajrhss-2192	108	19	(	(	PUNCT
ajrhss-2192	108	20	a	a	DET
ajrhss-2192	108	21	=	=	X
ajrhss-2192	108	22	p	p	X
ajrhss-2192	108	23	e^{rt	e^{rt	PROPN
ajrhss-2192	108	24	}	}	PUNCT
ajrhss-2192	108	25	\	\	NOUN
ajrhss-2192	108	26	)	)	PUNCT
ajrhss-2192	108	27	,	,	PUNCT
ajrhss-2192	108	28	where	where	SCONJ
ajrhss-2192	108	29	\	\	PROPN
ajrhss-2192	108	30	(	(	PUNCT
ajrhss-2192	108	31	p	p	PROPN
ajrhss-2192	108	32	\	\	PROPN
ajrhss-2192	108	33	)	)	PUNCT
ajrhss-2192	108	34	is	be	AUX
ajrhss-2192	108	35	the	the	DET
ajrhss-2192	108	36	principal	principal	ADJ
ajrhss-2192	108	37	amount	amount	NOUN
ajrhss-2192	108	38	,	,	PUNCT
ajrhss-2192	108	39	\	\	PROPN
ajrhss-2192	108	40	(	(	PUNCT
ajrhss-2192	108	41	r	r	NOUN
ajrhss-2192	108	42	\	\	NOUN
ajrhss-2192	108	43	)	)	PUNCT
ajrhss-2192	108	44	is	be	AUX
ajrhss-2192	108	45	the	the	DET
ajrhss-2192	108	46	rate	rate	NOUN
ajrhss-2192	108	47	,	,	PUNCT
ajrhss-2192	108	48	and	and	CCONJ
ajrhss-2192	108	49	\	\	PROPN
ajrhss-2192	108	50	(	(	PUNCT
ajrhss-2192	108	51	t	t	PROPN
ajrhss-2192	108	52	\	\	PROPN
ajrhss-2192	108	53	)	)	PUNCT
ajrhss-2192	108	54	is	be	AUX
ajrhss-2192	108	55	time	time	NOUN
ajrhss-2192	108	56	.	.	PUNCT
ajrhss-2192	109	1	2	2	X
ajrhss-2192	109	2	.	.	X
ajrhss-2192	109	3	continuous	continuous	ADJ
ajrhss-2192	109	4	compounding	compounding	NOUN
ajrhss-2192	109	5	:	:	PUNCT
ajrhss-2192	109	6	in	in	ADP
ajrhss-2192	109	7	continuous	continuous	ADJ
ajrhss-2192	109	8	compounding	compounding	NOUN
ajrhss-2192	109	9	,	,	PUNCT
ajrhss-2192	109	10	interest	interest	NOUN
ajrhss-2192	109	11	is	be	AUX
ajrhss-2192	109	12	compounded	compound	VERB
ajrhss-2192	109	13	continuously	continuously	ADV
ajrhss-2192	109	14	,	,	PUNCT
ajrhss-2192	109	15	leading	lead	VERB
ajrhss-2192	109	16	to	to	ADP
ajrhss-2192	109	17	the	the	DET
ajrhss-2192	109	18	formula	formula	NOUN
ajrhss-2192	109	19	\	\	PROPN
ajrhss-2192	109	20	(	(	PUNCT
ajrhss-2192	109	21	a	a	DET
ajrhss-2192	109	22	=	=	PUNCT
ajrhss-2192	109	23	pe^{rt	pe^{rt	PROPN
ajrhss-2192	109	24	}	}	PUNCT
ajrhss-2192	109	25	\	\	NOUN
ajrhss-2192	109	26	)	)	PUNCT
ajrhss-2192	109	27	.	.	PUNCT
ajrhss-2192	110	1	computer	computer	NOUN
ajrhss-2192	110	2	science	science	NOUN
ajrhss-2192	110	3	1	1	NUM
ajrhss-2192	110	4	.	.	PUNCT
ajrhss-2192	111	1	algorithms	algorithm	NOUN
ajrhss-2192	111	2	and	and	CCONJ
ajrhss-2192	111	3	complexity	complexity	NOUN
ajrhss-2192	111	4	:	:	PUNCT
ajrhss-2192	111	5	exponential	exponential	ADJ
ajrhss-2192	111	6	functions	function	NOUN
ajrhss-2192	111	7	describe	describe	VERB
ajrhss-2192	111	8	the	the	DET
ajrhss-2192	111	9	growth	growth	NOUN
ajrhss-2192	111	10	of	of	ADP
ajrhss-2192	111	11	certain	certain	ADJ
ajrhss-2192	111	12	algorithms	algorithm	NOUN
ajrhss-2192	111	13	'	'	PART
ajrhss-2192	111	14	time	time	NOUN
ajrhss-2192	111	15	complexity	complexity	NOUN
ajrhss-2192	111	16	,	,	PUNCT
ajrhss-2192	111	17	such	such	ADJ
ajrhss-2192	111	18	as	as	ADP
ajrhss-2192	111	19	those	those	PRON
ajrhss-2192	111	20	in	in	ADP
ajrhss-2192	111	21	combinatorial	combinatorial	ADJ
ajrhss-2192	111	22	problems	problem	NOUN
ajrhss-2192	111	23	.	.	PUNCT
ajrhss-2192	112	1	2	2	X
ajrhss-2192	112	2	.	.	X
ajrhss-2192	112	3	data	datum	NOUN
ajrhss-2192	112	4	modeling	modeling	NOUN
ajrhss-2192	112	5	:	:	PUNCT
ajrhss-2192	112	6	exponential	exponential	ADJ
ajrhss-2192	112	7	models	model	NOUN
ajrhss-2192	112	8	are	be	AUX
ajrhss-2192	112	9	used	use	VERB
ajrhss-2192	112	10	in	in	ADP
ajrhss-2192	112	11	machine	machine	NOUN
ajrhss-2192	112	12	learning	learning	NOUN
ajrhss-2192	112	13	and	and	CCONJ
ajrhss-2192	112	14	statistical	statistical	ADJ
ajrhss-2192	112	15	modeling	modeling	NOUN
ajrhss-2192	112	16	to	to	PART
ajrhss-2192	112	17	describe	describe	VERB
ajrhss-2192	112	18	phenomena	phenomenon	NOUN
ajrhss-2192	112	19	with	with	ADP
ajrhss-2192	112	20	rapid	rapid	ADJ
ajrhss-2192	112	21	growth	growth	NOUN
ajrhss-2192	112	22	or	or	CCONJ
ajrhss-2192	112	23	decay	decay	NOUN
ajrhss-2192	112	24	.	.	PUNCT
ajrhss-2192	113	1	theoretical	theoretical	ADJ
ajrhss-2192	113	2	importance	importance	NOUN
ajrhss-2192	113	3	1	1	NUM
ajrhss-2192	113	4	.	.	X
ajrhss-2192	113	5	solving	solve	VERB
ajrhss-2192	113	6	differential	differential	ADJ
ajrhss-2192	113	7	equations	equation	NOUN
ajrhss-2192	113	8	:	:	PUNCT
ajrhss-2192	113	9	many	many	ADJ
ajrhss-2192	113	10	physical	physical	ADJ
ajrhss-2192	113	11	systems	system	NOUN
ajrhss-2192	113	12	are	be	AUX
ajrhss-2192	113	13	modeled	model	VERB
ajrhss-2192	113	14	by	by	ADP
ajrhss-2192	113	15	differential	differential	ADJ
ajrhss-2192	113	16	equations	equation	NOUN
ajrhss-2192	113	17	where	where	SCONJ
ajrhss-2192	113	18	the	the	DET
ajrhss-2192	113	19	rate	rate	NOUN
ajrhss-2192	113	20	of	of	ADP
ajrhss-2192	113	21	change	change	NOUN
ajrhss-2192	113	22	of	of	ADP
ajrhss-2192	113	23	a	a	DET
ajrhss-2192	113	24	quantity	quantity	NOUN
ajrhss-2192	113	25	is	be	AUX
ajrhss-2192	113	26	proportional	proportional	ADJ
ajrhss-2192	113	27	to	to	ADP
ajrhss-2192	113	28	the	the	DET
ajrhss-2192	113	29	quantity	quantity	NOUN
ajrhss-2192	113	30	itself	itself	PRON
ajrhss-2192	113	31	.	.	PUNCT
ajrhss-2192	114	1	solutions	solution	NOUN
ajrhss-2192	114	2	to	to	ADP
ajrhss-2192	114	3	these	these	DET
ajrhss-2192	114	4	equations	equation	NOUN
ajrhss-2192	114	5	often	often	ADV
ajrhss-2192	114	6	involve	involve	VERB
ajrhss-2192	114	7	exponential	exponential	ADJ
ajrhss-2192	114	8	functions	function	NOUN
ajrhss-2192	114	9	.	.	PUNCT
ajrhss-2192	115	1	example	example	NOUN
ajrhss-2192	115	2	:	:	PUNCT
ajrhss-2192	115	3	the	the	DET
ajrhss-2192	115	4	differential	differential	ADJ
ajrhss-2192	115	5	equation	equation	NOUN
ajrhss-2192	115	6	\	\	PROPN
ajrhss-2192	115	7	(	(	PUNCT
ajrhss-2192	115	8	\frac{dy}{dx	\frac{dy}{dx	PROPN
ajrhss-2192	115	9	}	}	PUNCT
ajrhss-2192	115	10	=	=	SYM
ajrhss-2192	115	11	ky	ky	PROPN
ajrhss-2192	115	12	\	\	PROPN
ajrhss-2192	115	13	)	)	PUNCT
ajrhss-2192	115	14	has	have	VERB
ajrhss-2192	115	15	the	the	DET
ajrhss-2192	115	16	solution	solution	NOUN
ajrhss-2192	115	17	\	\	PROPN
ajrhss-2192	115	18	(	(	PUNCT
ajrhss-2192	115	19	y	y	NOUN
ajrhss-2192	115	20	=	=	PROPN
ajrhss-2192	115	21	ce^{kx}\	ce^{kx}\	NOUN
ajrhss-2192	115	22	)	)	PUNCT
ajrhss-2192	115	23	.	.	PUNCT
ajrhss-2192	116	1	2	2	X
ajrhss-2192	116	2	.	.	X
ajrhss-2192	116	3	stability	stability	NOUN
ajrhss-2192	116	4	analysis	analysis	NOUN
ajrhss-2192	116	5	:	:	PUNCT
ajrhss-2192	116	6	exponential	exponential	ADJ
ajrhss-2192	116	7	functions	function	NOUN
ajrhss-2192	116	8	help	help	VERB
ajrhss-2192	116	9	in	in	ADP
ajrhss-2192	116	10	analyzing	analyze	VERB
ajrhss-2192	116	11	the	the	DET
ajrhss-2192	116	12	stability	stability	NOUN
ajrhss-2192	116	13	of	of	ADP
ajrhss-2192	116	14	equilibrium	equilibrium	NOUN
ajrhss-2192	116	15	points	point	NOUN
ajrhss-2192	116	16	in	in	ADP
ajrhss-2192	116	17	dynamical	dynamical	ADJ
ajrhss-2192	116	18	systems	system	NOUN
ajrhss-2192	116	19	.	.	PUNCT
ajrhss-2192	117	1	solutions	solution	NOUN
ajrhss-2192	117	2	involving	involve	VERB
ajrhss-2192	117	3	\	\	PROPN
ajrhss-2192	117	4	(	(	PUNCT
ajrhss-2192	117	5	e^{\lambda	e^{\lambda	PROPN
ajrhss-2192	117	6	t	t	PROPN
ajrhss-2192	117	7	}	}	PUNCT
ajrhss-2192	117	8	\	\	NOUN
ajrhss-2192	117	9	)	)	PUNCT
ajrhss-2192	117	10	determine	determine	VERB
ajrhss-2192	117	11	the	the	DET
ajrhss-2192	117	12	behavior	behavior	NOUN
ajrhss-2192	117	13	near	near	ADP
ajrhss-2192	117	14	equilibrium	equilibrium	NOUN
ajrhss-2192	117	15	.	.	PUNCT
ajrhss-2192	118	1	3	3	X
ajrhss-2192	118	2	.	.	X
ajrhss-2192	118	3	fourier	fourier	NOUN
ajrhss-2192	118	4	transform	transform	NOUN
ajrhss-2192	118	5	:	:	PUNCT
ajrhss-2192	118	6	exponential	exponential	ADJ
ajrhss-2192	118	7	functions	function	NOUN
ajrhss-2192	118	8	,	,	PUNCT
ajrhss-2192	118	9	particularly	particularly	ADV
ajrhss-2192	118	10	complex	complex	ADJ
ajrhss-2192	118	11	exponentials	exponential	NOUN
ajrhss-2192	118	12	,	,	PUNCT
ajrhss-2192	118	13	are	be	AUX
ajrhss-2192	118	14	integral	integral	ADJ
ajrhss-2192	118	15	to	to	ADP
ajrhss-2192	118	16	fourier	fourier	ADJ
ajrhss-2192	118	17	analysis	analysis	NOUN
ajrhss-2192	118	18	,	,	PUNCT
ajrhss-2192	118	19	which	which	PRON
ajrhss-2192	118	20	decomposes	decompose	VERB
ajrhss-2192	118	21	functions	function	NOUN
ajrhss-2192	118	22	into	into	ADP
ajrhss-2192	118	23	their	their	PRON
ajrhss-2192	118	24	frequency	frequency	NOUN
ajrhss-2192	118	25	components	component	NOUN
ajrhss-2192	118	26	.	.	PUNCT
ajrhss-2192	119	1	advanced	advanced	ADJ
ajrhss-2192	119	2	concepts	concept	NOUN
ajrhss-2192	119	3	1	1	NUM
ajrhss-2192	119	4	.	.	PUNCT
ajrhss-2192	119	5	laplace	laplace	NOUN
ajrhss-2192	119	6	transform	transform	PROPN
ajrhss-2192	119	7	:	:	PUNCT
ajrhss-2192	119	8	the	the	DET
ajrhss-2192	119	9	laplace	laplace	NOUN
ajrhss-2192	119	10	transform	transform	NOUN
ajrhss-2192	119	11	,	,	PUNCT
ajrhss-2192	119	12	used	use	VERB
ajrhss-2192	119	13	to	to	PART
ajrhss-2192	119	14	solve	solve	VERB
ajrhss-2192	119	15	differential	differential	ADJ
ajrhss-2192	119	16	equations	equation	NOUN
ajrhss-2192	119	17	,	,	PUNCT
ajrhss-2192	119	18	is	be	AUX
ajrhss-2192	119	19	based	base	VERB
ajrhss-2192	119	20	on	on	ADP
ajrhss-2192	119	21	the	the	DET
ajrhss-2192	119	22	exponential	exponential	ADJ
ajrhss-2192	119	23	function	function	NOUN
ajrhss-2192	119	24	\	\	PROPN
ajrhss-2192	119	25	(	(	PUNCT
ajrhss-2192	119	26	e^{-st	e^{-st	ADJ
ajrhss-2192	119	27	}	}	PUNCT
ajrhss-2192	119	28	\	\	NOUN
ajrhss-2192	119	29	)	)	PUNCT
ajrhss-2192	119	30	.	.	PUNCT
ajrhss-2192	120	1	it	it	PRON
ajrhss-2192	120	2	transforms	transform	VERB
ajrhss-2192	120	3	a	a	DET
ajrhss-2192	120	4	function	function	NOUN
ajrhss-2192	120	5	of	of	ADP
ajrhss-2192	120	6	time	time	NOUN
ajrhss-2192	120	7	into	into	ADP
ajrhss-2192	120	8	a	a	DET
ajrhss-2192	120	9	function	function	NOUN
ajrhss-2192	120	10	of	of	ADP
ajrhss-2192	120	11	a	a	DET
ajrhss-2192	120	12	complex	complex	ADJ
ajrhss-2192	120	13	variable	variable	NOUN
ajrhss-2192	120	14	.	.	PUNCT
ajrhss-2192	121	1	2	2	X
ajrhss-2192	121	2	.	.	X
ajrhss-2192	121	3	eigenvalues	eigenvalue	NOUN
ajrhss-2192	121	4	and	and	CCONJ
ajrhss-2192	121	5	eigenvectors	eigenvector	NOUN
ajrhss-2192	121	6	:	:	PUNCT
ajrhss-2192	121	7	in	in	ADP
ajrhss-2192	121	8	linear	linear	PROPN
ajrhss-2192	121	9	algebra	algebra	NOUN
ajrhss-2192	121	10	,	,	PUNCT
ajrhss-2192	121	11	solving	solve	VERB
ajrhss-2192	121	12	systems	system	NOUN
ajrhss-2192	121	13	of	of	ADP
ajrhss-2192	121	14	linear	linear	PROPN
ajrhss-2192	121	15	differential	differential	ADJ
ajrhss-2192	121	16	equations	equation	NOUN
ajrhss-2192	121	17	involves	involve	VERB
ajrhss-2192	121	18	finding	find	VERB
ajrhss-2192	121	19	eigenvalues	eigenvalue	NOUN
ajrhss-2192	121	20	and	and	CCONJ
ajrhss-2192	121	21	eigenvectors	eigenvector	NOUN
ajrhss-2192	121	22	,	,	PUNCT
ajrhss-2192	121	23	which	which	PRON
ajrhss-2192	121	24	often	often	ADV
ajrhss-2192	121	25	result	result	VERB
ajrhss-2192	121	26	in	in	ADP
ajrhss-2192	121	27	exponential	exponential	ADJ
ajrhss-2192	121	28	solutions	solution	NOUN
ajrhss-2192	121	29	.	.	PUNCT
ajrhss-2192	122	1	3	3	X
ajrhss-2192	122	2	.	.	X
ajrhss-2192	122	3	probability	probability	NOUN
ajrhss-2192	122	4	theory	theory	NOUN
ajrhss-2192	122	5	:	:	PUNCT
ajrhss-2192	122	6	the	the	DET
ajrhss-2192	122	7	exponential	exponential	ADJ
ajrhss-2192	122	8	distribution	distribution	NOUN
ajrhss-2192	122	9	models	model	NOUN
ajrhss-2192	122	10	the	the	DET
ajrhss-2192	122	11	time	time	NOUN
ajrhss-2192	122	12	between	between	ADP
ajrhss-2192	122	13	events	event	NOUN
ajrhss-2192	122	14	in	in	ADP
ajrhss-2192	122	15	a	a	DET
ajrhss-2192	122	16	poisson	poisson	NOUN
ajrhss-2192	122	17	process	process	NOUN
ajrhss-2192	122	18	and	and	CCONJ
ajrhss-2192	122	19	has	have	VERB
ajrhss-2192	122	20	a	a	DET
ajrhss-2192	122	21	constant	constant	ADJ
ajrhss-2192	122	22	hazard	hazard	NOUN
ajrhss-2192	122	23	rate	rate	NOUN
ajrhss-2192	122	24	,	,	PUNCT
ajrhss-2192	122	25	meaning	mean	VERB
ajrhss-2192	122	26	the	the	DET
ajrhss-2192	122	27	event	event	NOUN
ajrhss-2192	122	28	rate	rate	NOUN
ajrhss-2192	122	29	is	be	AUX
ajrhss-2192	122	30	constant	constant	ADJ
ajrhss-2192	122	31	over	over	ADP
ajrhss-2192	122	32	time	time	NOUN
ajrhss-2192	122	33	.	.	PUNCT
ajrhss-2192	123	1	american	american	ADJ
ajrhss-2192	123	2	journal	journal	PROPN
ajrhss-2192	123	3	of	of	ADP
ajrhss-2192	123	4	research	research	NOUN
ajrhss-2192	123	5	in	in	ADP
ajrhss-2192	123	6	humanities	humanity	NOUN
ajrhss-2192	123	7	and	and	CCONJ
ajrhss-2192	123	8	social	social	ADJ
ajrhss-2192	123	9	sciences	science	NOUN
ajrhss-2192	123	10	volume	volume	NOUN
ajrhss-2192	123	11	25	25	NUM
ajrhss-2192	123	12	june	june	PROPN
ajrhss-2192	123	13	2024	2024	NUM
ajrhss-2192	123	14	p	p	NOUN
ajrhss-2192	123	15	a	a	PRON
ajrhss-2192	123	16	g	g	NOUN
ajrhss-2192	123	17	e	e	NOUN
ajrhss-2192	124	1	|	|	ADV
ajrhss-2192	124	2	37	37	NUM
ajrhss-2192	124	3	www.americanjournal.org	www.americanjournal.org	NOUN
ajrhss-2192	124	4	conclusion	conclusion	NOUN
ajrhss-2192	124	5	exponential	exponential	NOUN
ajrhss-2192	124	6	functions	function	NOUN
ajrhss-2192	124	7	are	be	AUX
ajrhss-2192	124	8	foundational	foundational	ADJ
ajrhss-2192	124	9	in	in	ADP
ajrhss-2192	124	10	mathematics	mathematic	NOUN
ajrhss-2192	124	11	due	due	ADP
ajrhss-2192	124	12	to	to	ADP
ajrhss-2192	124	13	their	their	PRON
ajrhss-2192	124	14	unique	unique	ADJ
ajrhss-2192	124	15	properties	property	NOUN
ajrhss-2192	124	16	and	and	CCONJ
ajrhss-2192	124	17	broad	broad	ADJ
ajrhss-2192	124	18	applicability	applicability	NOUN
ajrhss-2192	124	19	.	.	PUNCT
ajrhss-2192	125	1	they	they	PRON
ajrhss-2192	125	2	are	be	AUX
ajrhss-2192	125	3	essential	essential	ADJ
ajrhss-2192	125	4	in	in	ADP
ajrhss-2192	125	5	modeling	modeling	NOUN
ajrhss-2192	125	6	and	and	CCONJ
ajrhss-2192	125	7	solving	solve	VERB
ajrhss-2192	125	8	problems	problem	NOUN
ajrhss-2192	125	9	across	across	ADP
ajrhss-2192	125	10	diverse	diverse	ADJ
ajrhss-2192	125	11	fields	field	NOUN
ajrhss-2192	125	12	such	such	ADJ
ajrhss-2192	125	13	as	as	ADP
ajrhss-2192	125	14	physics	physics	NOUN
ajrhss-2192	125	15	,	,	PUNCT
ajrhss-2192	125	16	biology	biology	NOUN
ajrhss-2192	125	17	,	,	PUNCT
ajrhss-2192	125	18	finance	finance	NOUN
ajrhss-2192	125	19	,	,	PUNCT
ajrhss-2192	125	20	and	and	CCONJ
ajrhss-2192	125	21	engineering	engineering	NOUN
ajrhss-2192	125	22	.	.	PUNCT
ajrhss-2192	126	1	their	their	PRON
ajrhss-2192	126	2	ability	ability	NOUN
ajrhss-2192	126	3	to	to	PART
ajrhss-2192	126	4	describe	describe	VERB
ajrhss-2192	126	5	rapid	rapid	ADJ
ajrhss-2192	126	6	changes	change	NOUN
ajrhss-2192	126	7	,	,	PUNCT
ajrhss-2192	126	8	both	both	CCONJ
ajrhss-2192	126	9	growth	growth	NOUN
ajrhss-2192	126	10	and	and	CCONJ
ajrhss-2192	126	11	decay	decay	NOUN
ajrhss-2192	126	12	,	,	PUNCT
ajrhss-2192	126	13	makes	make	VERB
ajrhss-2192	126	14	them	they	PRON
ajrhss-2192	126	15	indispensable	indispensable	ADJ
ajrhss-2192	126	16	tools	tool	NOUN
ajrhss-2192	126	17	for	for	ADP
ajrhss-2192	126	18	mathematicians	mathematician	NOUN
ajrhss-2192	126	19	and	and	CCONJ
ajrhss-2192	126	20	scientists	scientist	NOUN
ajrhss-2192	126	21	.	.	PUNCT
ajrhss-2192	127	1	references	reference	NOUN
ajrhss-2192	127	2	1	1	NUM
ajrhss-2192	127	3	.	.	PUNCT
ajrhss-2192	127	4	sharafiddinov	sharafiddinov	NOUN
ajrhss-2192	127	5	zokir	zokir	PROPN
ajrhss-2192	127	6	.	.	PUNCT
ajrhss-2192	128	1	matematik	matematik	PROPN
ajrhss-2192	128	2	tahlil	tahlil	PROPN
ajrhss-2192	128	3	va	va	PROPN
ajrhss-2192	128	4	ko’rsatkichli	ko’rsatkichli	VERB
ajrhss-2192	128	5	funksiyalar,2015	funksiyalar,2015	PROPN
ajrhss-2192	128	6	2	2	NUM
ajrhss-2192	128	7	.	.	PUNCT
ajrhss-2192	128	8	nizomov	nizomov	PROPN
ajrhss-2192	128	9	karim	karim	PROPN
ajrhss-2192	128	10	.	.	PUNCT
ajrhss-2192	129	1	algebra	algebra	PROPN
ajrhss-2192	129	2	va	va	PROPN
ajrhss-2192	129	3	ko’rsatkichli	ko’rsatkichli	VERB
ajrhss-2192	129	4	funksiyalar,2022	funksiyalar,2022	NOUN
ajrhss-2192	129	5	3	3	NUM
ajrhss-2192	129	6	.	.	PUNCT
ajrhss-2192	129	7	aminov	aminov	ADJ
ajrhss-2192	129	8	bahodir	bahodir	PROPN
ajrhss-2192	129	9	.	.	PUNCT
ajrhss-2192	130	1	differensial	differensial	ADJ
ajrhss-2192	130	2	tenglamalar	tenglamalar	PROPN
ajrhss-2192	130	3	va	va	PROPN
ajrhss-2192	130	4	ko’rsatkichli	ko’rsatkichli	VERB
ajrhss-2192	130	5	funksiyalar	funksiyalar	ADJ
ajrhss-2192	130	6	,	,	PUNCT
ajrhss-2192	130	7	2021	2021	NUM
ajrhss-2192	130	8	4	4	NUM
ajrhss-2192	131	1	.	.	PUNCT
ajrhss-2192	131	2	stewart	stewart	PROPN
ajrhss-2192	131	3	,	,	PUNCT
ajrhss-2192	131	4	james	james	PROPN
ajrhss-2192	131	5	.	.	PUNCT
ajrhss-2192	132	1	*	*	PUNCT
ajrhss-2192	132	2	calculus	calculus	NOUN
ajrhss-2192	132	3	:	:	PUNCT
ajrhss-2192	132	4	early	early	ADJ
ajrhss-2192	132	5	transcendentals	transcendental	NOUN
ajrhss-2192	132	6	*	*	PROPN
ajrhss-2192	132	7	.	.	PUNCT
ajrhss-2192	133	1	cengage	cengage	PROPN
ajrhss-2192	133	2	learning	learning	PROPN
ajrhss-2192	133	3	,	,	PUNCT
ajrhss-2192	133	4	2015	2015	NUM
ajrhss-2192	133	5	.	.	PUNCT
ajrhss-2192	134	1	5	5	NUM
ajrhss-2192	134	2	.	.	X
ajrhss-2192	134	3	strang	strang	PROPN
ajrhss-2192	134	4	,	,	PUNCT
ajrhss-2192	134	5	gilbert	gilbert	PROPN
ajrhss-2192	134	6	.	.	PUNCT
ajrhss-2192	135	1	*	*	PUNCT
ajrhss-2192	135	2	introduction	introduction	NOUN
ajrhss-2192	135	3	to	to	AUX
ajrhss-2192	135	4	linear	linear	PROPN
ajrhss-2192	135	5	algebra	algebra	PROPN
ajrhss-2192	135	6	*	*	PUNCT
ajrhss-2192	135	7	.	.	PUNCT
ajrhss-2192	136	1	wellesley	wellesley	PROPN
ajrhss-2192	136	2	-	-	PUNCT
ajrhss-2192	136	3	cambridge	cambridge	PROPN
ajrhss-2192	136	4	press	press	NOUN
ajrhss-2192	136	5	,	,	PUNCT
ajrhss-2192	136	6	2016	2016	NUM
ajrhss-2192	136	7	.	.	PUNCT
ajrhss-2192	137	1	6	6	NUM
ajrhss-2192	137	2	.	.	X
ajrhss-2192	137	3	thomas	thomas	PROPN
ajrhss-2192	137	4	,	,	PUNCT
ajrhss-2192	137	5	george	george	PROPN
ajrhss-2192	137	6	b.	b.	PROPN
ajrhss-2192	137	7	,	,	PUNCT
ajrhss-2192	137	8	et	et	PROPN
ajrhss-2192	137	9	al	al	PROPN
ajrhss-2192	137	10	.	.	PUNCT
ajrhss-2192	138	1	*	*	PUNCT
ajrhss-2192	138	2	thomas	thomas	PROPN
ajrhss-2192	138	3	'	'	PART
ajrhss-2192	138	4	calculus	calculus	PROPN
ajrhss-2192	138	5	*	*	PUNCT
ajrhss-2192	138	6	.	.	PUNCT
ajrhss-2192	139	1	pearson	pearson	PROPN
ajrhss-2192	139	2	,	,	PUNCT
ajrhss-2192	139	3	2016	2016	NUM
ajrhss-2192	139	4	.	.	PUNCT
ajrhss-2192	140	1	7	7	X
ajrhss-2192	140	2	.	.	X
ajrhss-2192	140	3	boyce	boyce	PROPN
ajrhss-2192	140	4	,	,	PUNCT
ajrhss-2192	140	5	william	william	PROPN
ajrhss-2192	140	6	e.	e.	PROPN
ajrhss-2192	140	7	,	,	PUNCT
ajrhss-2192	140	8	and	and	CCONJ
ajrhss-2192	140	9	richard	richard	PROPN
ajrhss-2192	140	10	c.	c.	PROPN
ajrhss-2192	140	11	diprima	diprima	PROPN
ajrhss-2192	140	12	.	.	PUNCT
ajrhss-2192	141	1	*	*	PUNCT
ajrhss-2192	141	2	elementary	elementary	ADJ
ajrhss-2192	141	3	differential	differential	ADJ
ajrhss-2192	141	4	equations	equation	NOUN
ajrhss-2192	141	5	and	and	CCONJ
ajrhss-2192	141	6	boundary	boundary	ADJ
ajrhss-2192	141	7	value	value	NOUN
ajrhss-2192	141	8	problems	problem	NOUN
ajrhss-2192	141	9	*	*	PUNCT
ajrhss-2192	141	10	.	.	PUNCT
ajrhss-2192	142	1	wiley	wiley	PROPN
ajrhss-2192	142	2	,	,	PUNCT
ajrhss-2192	142	3	2017	2017	NUM
ajrhss-2192	142	4	.	.	PUNCT
ajrhss-2192	143	1	8	8	NUM
ajrhss-2192	143	2	.	.	X
ajrhss-2192	143	3	murray	murray	PROPN
ajrhss-2192	143	4	,	,	PUNCT
ajrhss-2192	143	5	james	james	PROPN
ajrhss-2192	143	6	d.	d.	PROPN
ajrhss-2192	143	7	*	*	PROPN
ajrhss-2192	143	8	mathematical	mathematical	ADJ
ajrhss-2192	143	9	biology	biology	NOUN
ajrhss-2192	143	10	*	*	NOUN
ajrhss-2192	143	11	.	.	PUNCT
ajrhss-2192	143	12	springer	springer	NOUN
ajrhss-2192	143	13	,	,	PUNCT
ajrhss-2192	143	14	2002	2002	NUM
ajrhss-2192	143	15	.	.	PUNCT
ajrhss-2192	144	1	9	9	X
ajrhss-2192	144	2	.	.	X
ajrhss-2192	144	3	ross	ross	PROPN
ajrhss-2192	144	4	,	,	PUNCT
ajrhss-2192	144	5	sheldon	sheldon	PROPN
ajrhss-2192	144	6	m.	m.	PROPN
ajrhss-2192	144	7	*	*	PUNCT
ajrhss-2192	144	8	a	a	DET
ajrhss-2192	144	9	first	first	ADJ
ajrhss-2192	144	10	course	course	NOUN
ajrhss-2192	144	11	in	in	ADP
ajrhss-2192	144	12	probability	probability	NOUN
ajrhss-2192	144	13	*	*	X
ajrhss-2192	144	14	.	.	PUNCT
ajrhss-2192	145	1	pearson	pearson	PROPN
ajrhss-2192	145	2	,	,	PUNCT
ajrhss-2192	145	3	2014	2014	NUM
ajrhss-2192	145	4	.	.	PUNCT
ajrhss-2192	146	1	10	10	NUM
ajrhss-2192	146	2	.	.	X
ajrhss-2192	146	3	brigham	brigham	PROPN
ajrhss-2192	146	4	,	,	PUNCT
ajrhss-2192	146	5	e.	e.	PROPN
ajrhss-2192	146	6	o.	o.	PROPN
ajrhss-2192	147	1	*	*	PROPN
ajrhss-2192	147	2	the	the	DET
ajrhss-2192	147	3	fast	fast	ADJ
ajrhss-2192	147	4	fourier	fourier	NOUN
ajrhss-2192	147	5	transform	transform	NOUN
ajrhss-2192	147	6	and	and	CCONJ
ajrhss-2192	147	7	its	its	PRON
ajrhss-2192	147	8	applications	application	NOUN
ajrhss-2192	147	9	*	*	PUNCT
ajrhss-2192	147	10	.	.	PUNCT
ajrhss-2192	148	1	prentice	prentice	NOUN
ajrhss-2192	148	2	-	-	PUNCT
ajrhss-2192	148	3	hall	hall	NOUN
ajrhss-2192	148	4	,	,	PUNCT
ajrhss-2192	148	5	1988	1988	NUM
ajrhss-2192	148	6	.	.	PUNCT