Math 22 Natural Exponential Functions

Limit Definition of $e$

 The irrational number $e$ is defined to be the limit:
 $\lim _{x\to 0}(1+x)^{\frac {1}{x}}=e$
 $e\approx 2.71828182846$

Compound Interest

 Let $P$ be the amount deposited, $t$ the number of years, $A$ the balance, and $r$ the annual interest rate (in decimal form).
 1. Compounded $n$ times per year: $A=P(1+{\frac {r}{n}})^{rt}$
 2. Compounded continuously: $A=Pe^{rt}$

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