Answer
a) $P=10,000 e^{0.04 t}$
b) The population after 5 years is about $12,214$.
c) $4.08 \%$
Work Step by Step
(a) The number of residents, $P$, in the town after $t$ years is given by
$$
P=10,000 e^{0.04 t}
$$
(b)Set $t=5$ into our population formula, we obtain
$$
P=10,000 e^{0.04(5)}=12,214.028
$$
The population after 5 years is about $ 12,214$.
c)
$$
\begin{aligned}
&10,000 e^{0.04 t}=10,000\left(e^{0.04}\right)^t=10,000(1.0408)^t,\\
&\text { the annual growth rate is } 1.0408-1=0.0408 \text {, or } 4.08 \% \text {. }
\end{aligned}
$$
