Answer
(a) $n(t)=12e^{0.012t}$
(b) $12.742$ million
(c) $12.846$ years
(d) see graph.
Work Step by Step
(a) Using model $n(t)=n_0e^{rt}$, set $t=0$ for 2010, we have $n_0=12, r=0.012$ and
the function becomes $n(t)=12e^{0.012t}$
(b) Let $t=5$ for 2015, we have $n(5)=12e^{0.012\times5}=12.742$ million
(c) Let $n(t)=14$, we have $12e^{0.012t}=14$, solve for t we get $t=ln(14/12)/0.012=12.846$ years
(d) The above function can be graphed as shown in the figure.
