Question

What is the fox population predicted to be in the year 2020?

Answer 1

The exponential growth model is given to be:

`f(x)=a(1+r)^x`

where a is the initial amount and r is the growth rate in decimals.

The growth rate is given to be 9% per year. This means that:

`r=(9)/(100)=0.09`

In the year 2012, there were 22,900 foxes. This means that:

`a=22900`

Therefore, the model will be:

`\begin{gathered} f(x)=22900(1+0.09)^x \\ f(x)=22900(1.09)^x \end{gathered}`

where f(x) is the fox population after x years after 2012.

The year 2020 is 8 years after 2012.

Therefore, the fox population will be:

`\begin{gathered} x=8 \\ \therefore \\ f(x)=22900(1.09)^8 \\ f(x)=45629.68 \end{gathered}`

The estimated fox population is 45,630.