id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ajrhss-2192	Abdurashitov Rakhmatullo Abdukhamitovich; Khusenov Zikrillo Raxmatillo ogli; Adkhamov Khasanboy Abdusalom ogli	EXPONENTIAL FUNCTION	2024	8	.pdf	application/pdf	2244	150	44	Population at time \( t \) - \( P_0 \): Initial population - \( r \): Growth rate - \( t \): Time - Exponential Decay Model: \( N(t) = N_0 e^{-kt} \) - \( N(t) \): Quantity at time \( t \) - \( N_0 \): Initial quantity - \( k \): Decay constant - \( t \): Time Understanding these concepts helps in analyzing and interpreting various natural and financial phenomena that exhibit exponential behavior. The most common base for exponential functions in mathematics is \( e \) (approximately 2.71828), leading to the natural exponential function \( f(x) = e^x \).	cache/ajrhss-2192.pdf	txt/ajrhss-2192.txt