Chapter 4 - Exponential Functions - 4.5 The Number e - Exercises and Problems for Section 4.5 - Exercises and Problems - Page 173: 21

a) $P(t)=25,000 e^{0.075 t}$ b) The population increases by $7.788\%$ each year.

Using $P=P_0 e^{k t}$ where $P_0=25,000$ and $k=7.5 \%$, we have $$ P(t)=25,000 e^{0.075 t} $$ (b) We first find the growth factor from $$ P=25,000 e^{0.075 t}=25,000\left(e^{0.075}\right)^t \approx 25,000(1.07788)^t $$ The population increases by $7.788\%$ each year.