Answer
(a) $n(t)=1000e^{2.07944t}$
(b) $22627$
(c) $1.3$
(d) see graph below.
Work Step by Step
(a) Given $n_0=1000, n(1)=8000$ we have $1000e^r=8000$ which gives $r=2.07944$
Thus, the function can be written as $n(t)=1000e^{2.07944t}$
(b) At $t=1.5$, $n(1.5)=1000e^{2.07944\times1.5}\approx22627$
(c) Let $n(t)=1000e^{2.07944t}=15000$, we can solve $t$ which gives $t=ln(15)/2.07944\approx1.3$
(d) The above function can be graphed as shown in the figure.
