Answer
(a) $n(t)=30e^{0.15t}$
(b) $55$
(c) $19$ years
Work Step by Step
(a)We can model the growth with the exponential formula $n(t)=n_0e^{rt}$
with $n_0=30,r=0.15$, we have $n(t)=30e^{0.15t}$
(b) Let $t=4$, we have $n(4)=30e^{0.15\times4}\approx55$
(c) Let $n(t)=500$, we have $30e^{0.15t}=500$ which gives $t=ln(500/30)/0.15\approx19$ years
