Answer
(a) $n(t)=29.76e^{0.012936t}$
(b) $53.6$ years
(c) $38.55$ million
Work Step by Step
(a) Use the exponential model equation $n(t)=n_0e^{rt}$ and the given conditions
$n_0=29.76, n(10)=33.87$, we have $33.87=29.76e^{10r}$ which gives $r=ln(33.87/29.76)/10\approx0.012936$
thus the model equation can be written as $n(t)=29.76e^{0.012936t}$
(b) Let $n(t)=2n_0$, we get $2n_0=n_0e^{0.0129t}$ so that $t=ln2/0.012936\approx53.6$ years
(c) As 2010 corresponds to $t=20$, we have $n(20)=29.76e^{0.012936\times20}\approx38.55$ million
