Chapter 12 - Exponential Functions and Logarithmic Functions - 12.7 Applications of Exponential Functions and Logarithmic Functions - 12.7 Exercise Set - Page 833: 4

A

Consider the model $P\left( t \right)={{P}_{0}}{{e}^{kt}},k>0$. Here, ${{P}_{0}}$ is the population at time 0, $P\left( t \right)$ is the population at time $t$, $k$ is the exponential growth rate, and doubling time is the amount of time necessary for the population to double in size. Thus, the variable T, where $2{{P}_{0}}={{P}_{0}}{{e}^{kt}}$ matches with option a.