The exponential growth model is given to be:
[tex]f(x)=a(1+r)^x[/tex]
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:
[tex]r=\frac{9}{100}=0.09[/tex]
In the year 2012, there were 22,900 foxes. This means that:
[tex]a=22900[/tex]
Therefore, the model will be:
[tex]\begin{gathered} f(x)=22900(1+0.09)^x \\ f(x)=22900(1.09)^x \end{gathered}[/tex]
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:
[tex]\begin{gathered} x=8 \\ \therefore \\ f(x)=22900(1.09)^8 \\ f(x)=45629.68 \end{gathered}[/tex]
The estimated fox population is 45,630.
