Chapter 3 - Section 3.5 - Exponential Growth and Decay; Modeling Data - Exercise Set - Page 506: 34

$ 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.