Answer
(a) $n(t)=350000\cdot 2^{t/25}$
(b) $n(t)=350000\cdot e^{0.0277t}$
(c) see graph.
(d) $63$ years
Work Step by Step
(a) Given $n_0=350000,n(25)=2n_0$, we have $2n_0=n_02^{25/a}$ which gives $a=25$
thus the exponential model is $n(t)=350000\cdot 2^{t/25}$
(b) For this case, $2n_0=n_0e^{25r}$ and we can find $r=ln2/25=0.0277$
thus this exponential model can be written as $n(t)=350000\cdot e^{0.0277t}$
(c) The functions defined above can be graphed as shown in the figure.
(d) Let $n(t)=2000000$, we have $350000e^{0.0277t}=2000000$ and we can find that
$t=ln(200/35)/0.0277=62.9\approx63$ years