Answer
(a) $n(t)=18000e^{0.08t}$
(b) $34137$
(c) $t=4.1$ years
(d) See graph below.
Work Step by Step
(a) Use the exponential growth model $n(t)=n_0e^{0.08t}$ with $n_0$ being the initial population.
Set $t=0$ for year 2013, we have $n_0=18000$, thus the function for the population after 2013
is given by $n(t)=18000e^{0.08t}$
(b) Use the function from part (a) to estimate the fox population in the year 2021.
For year 2021, $t=2021-2013=8$, and $n(8)=18000e^{0.08\times8}=34136.65\approx34137$
(c) After how many years will the fox population reach 25,000?
Let $18000e^{0.08t}=25000$, we have $0.08t=ln(25/18)=0.3285$, thus $t=4.1$ years
(d) The fox population function for the years 2013–2021 can be graphed as shown in the figure.
