## Precalculus (6th Edition) Blitzer

$0.0174$
Exponential growth model $: \quad A= A_{0}e^{kt}$. If $k \gt 0$, the function models the amount of a growing entity. $A_{0}$ is the original amount, or size, of the growing entity at time t = 0, $A$ is the amount at time $t$, and $k$ is a constant representing the growth rate. If k is negative, the model is an exponential decay model. ---- Model: $A=A_{0}e^{kt}$ $t=0$ for the year $2010.$ Unknown: $k$, when $A_{0}=21.3, A=42.7, t=40,$ $42.7=21.3e^{k\cdot 40}\qquad$... /$\div 21.3$ $2.0047\approx e^{k\cdot 40}\qquad$... $/\ln(...)$ $0.69549=40k\qquad$... /$\div 40$ $k\approx 0.0174$