Answer
(a). $n(t)=30e^{0.15t}$
(b). $n(4)=54.66$
(c).$t=18.75$ year
Work Step by Step
The formula for exponential population growth is, $n(t)=n_0e^{rt}$. Whereas, $n_0$ is the Initial population, $r$ is the growth rate, and $n(t)$ is the population at time $t$.
$n(t)=n_0e^{rt}$,
$n_0=30$, $r=0.15$
(a). $n(t)=30e^{0.15t}$
(b). $n(4)=30e^{0.15\times4}=54.66$
(c). $500=30e^{0.15t}$,
$16.66=e^{0.15t}$,
$\ln 16.66=0.15t$,
$t=18.75$ year
