Question

The fox population in a certain region has a continuous growth rate of 9 percent per year.

Answer 1

SOLUTION

The function can be derived from the model

$\begin{gathered} P=P_oe^{(\ln r)t^{}} \\ \\ r\text{ here represents 1 + 9 percent growth rate } \end{gathered}$

So the function becomes

$P(t)=2000_{}e^{(\ln 1.09)t}$

So the fox population in 2008

2008 - 2000 = 8

So our t becomes 8

The population becomes

$\begin{gathered} P=2000_{}e^{(\ln 1.09)t} \\ P=2000_{}e^{(\ln 1.09)\times8} \\ P=\text{ }2000_{}e^{0.086177\times8} \\ =2000_{}e^{0.6894} \\ =\text{ 3985.04} \end{gathered}$

So the Population = 3985