Question

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

Answer 1

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)*8) \\ P=\text{ }2000_{}e^(0.086177*8) \\ =2000_{}e^(0.6894) \\ =\text{ 3985.04} \end{gathered}`

So the Population = 3985