Answer
(a) $n(t)=8600e^{0.1508t}$
(b) $11627$
(c) $4.6$ hours
Work Step by Step
(a) Using an exponential model $n(t)=n_0e^{rt}$, given $n_0=8600, n(1)=10000$,
we have $10000=8600e^r$, thus we can find $r=ln(100/86)=0.1508$ so we can
rewrite the function as $n(t)=8600e^{0.1508t}$
(b) Let $t=2$, we have $n(2)=8600e^{0.1508\times2}\approx11627$
(c) Let $n(t)=2n_0$, we have $2n_0=n_0e^{0.1508t}$ which gives $t=ln2/0.1508\approx4.6$ hours
