College Algebra, Chapter 5, 5.5, Section 5.5, Problem 4

The estimated population of a Fox in 2005 at Hokkaido, Japan is $18,000$, the relative growth rate of the Fox is $8\%$ per year.

a.) Determine a function that will model the population t years after 2005.

b.) By using the function in part(a) estimate the population of the Fox in year 2013.

c.) Graph the Fox population for the years 2005-2013.




a.) Recall the formula for growth rate

$n(t) = n_0 e^{rt}$

where

$n(t)$ = population at time $t$

$n_0$ = initial size of the population

$r$ = relative rate of growth

$t$ = time

If we let the population of the fox at 2005 be its initial population, then the model of the fox's population after $t$ years is

$n(t) = 18000 e^{0.08t}$

b.) @ 2013, $t = 8$


$
\begin{equation}
\begin{aligned}

n(8) =& 1800 e^{0.08(8)}
\\
\\
n(8) =& 34136.66 \text{ or } 34136

\end{aligned}
\end{equation}
$


c.)