## Precalculus (6th Edition) Blitzer

$t=\displaystyle \frac{\ln 3}{k}$ is the time needed for the population to triple.
Model: $A=A_{0}e^{kt}$ Unknown: $t$, when $A=3A_{0}$ $3A_{0}=A_{0}e^{kt}\qquad... /\div A_{0}$ $3=e^{kt}\qquad.../\ln(...)$ $\ln 3=kt\qquad.../\div k$ $t=\displaystyle \frac{\ln 3}{k}$ is the time needed for the population to triple.