Answer
(a).$n_0=100$
(b).$n(t)=100e^{0.41t}$
(c).$n(15)=46,871.74$
(d).$t=16.15$
Work Step by Step
$n(t)=n_0\times e^{rt}$. Whereas,$n(t)$ is population at time $t$, $n_0$ is Initial size of the population, $r$ is relative rate of growth, and $t$ is time.
(a). From the graph we can estimate that $n_0=100$
(b). $n_0=100$, $n(2)=225$.
$100e^{2r}=225$,
$e^{2r}=2.25$,
$2r=\ln 2.25$,
$r=0.41$.
Therefore, $n(t)=100e^{0.41t}$
(c). $n(15)=100e^{0.41\times15}=46,871.74$
(d). $n(t)=100e^{0.41t}=75,000$
$e^{0.41t}=750$,
$0.41t=\ln 750$,
$t=16.15$
