Answer
(a). $20,000$
(b).$n(t)=20,000 \times e^{0.11t}$
(c).$n(8)=48,217.99$
(d).$t=14.63$
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 observe that the population at $2010$ is $20,000$
(b).$n_0=20,000$, $t=4$, $n(4)=31,000$.
$n(4)=20000\times e^{4r}=31,000$
$e^{4r}=1.55$
$4r=\ln1.55$
$r=0.11$.
Therefore, $n(t)=20,000 \times e^{0.11t}$.
(c).In 2018, $t=8$.
$n(8)=20000 \times e^{0.11\times8}=48,217.99$
(d).$n(t)=100,000$
$n(t)=20,000\times e^{0.11t}=100,000$
$e^{0.11t}=5$
$0.11t=\ln5$
$t=14.63$
