Chapter 3 - Section 3.5 - Exponential Growth and Decay; Modeling Data - Exercise Set - Page 506: 33

$ t=\displaystyle \frac{\ln 2}{k}$ is the time needed for the population to double.

Model: $ A=A_{0}e^{kt}$ Unknown: $ t $, when $ A=2A_{0}$ $2A_{0}=A_{0}e^{kt}\qquad... /\div A_{0}$ $2=e^{kt}\qquad.../\ln(...)$ $\ln 2=kt\qquad.../\div k $ $ t=\displaystyle \frac{\ln 2}{k}$ is the time needed for the population to double.