## College Algebra (6th Edition)

Exponential growth model: $A=A_{0}e^{kt} \qquad(k>0)$ ($A_{0}$ is the initial quantity, $A$ is the quantity after time t). We solve for t (the time it takes for $A$ to become 3$A_{0}$). $3A_{0}=A_{0}e^{k\mathrm{r}}\displaystyle \qquad .../\times\frac{1}{A_{o}}$ $3=e^{k\mathrm{r}}\qquad .../$ take ln( ) of both sides $\mathrm{l}\mathrm{n}3 =kt$ $t=\displaystyle \frac{\ln 3}{k}$ The population will triple in $t=\displaystyle \frac{\ln 3}{k}$ years, which confirms the problem statement.