Answer
(a) $n(t)=112000\cdot 2^{t/18}$
(b) $n(t)=112000e^{0.0385t}$
(c) see graph
(d) $38.9$ years
Work Step by Step
(a) Given $n_0=112000, n(18)=2n_0$, we have $2n_0=n_0\cdot 2^{18/a}$ which gives $a=18$
and the exponential model for the population is $n(t)=112000\cdot 2^{t/18}$
(b) For model $n(t)=n_0e^{rt}$, let $t=18, n(18)=2n_0$, we have $2n_0=n_0e^{18r}$ which gives
$r=0.0385$ and the population equation becomes $n(t)=112000e^{0.0385t}$
(c) Function defined in (a) can be graphed as shown in the figure.
(d) Let $n(t)=500000$, using equation in (a), we have $112000\cdot 2^{t/18}=500000$
which gives $t=18\times log_2(500/112)\approx38.9$ years
