If the population is declining by 13% every year, this means that at the end of the year the population is 87% of the population at the start of the year.
This is an exponential behavior expressed as:
[tex]P(t)=A\cdot b^t[/tex]Where P(t) is the population of foxes after t years, A is the initial population, and b is the percentage (87% in this case). From the problem, we identify:
[tex]\begin{gathered} A=3670 \\ b=0.87 \end{gathered}[/tex]The final model is:
[tex]P(t)=3670\cdot0.87^t[/tex]After 8 years (t = 8), the population will be (to the nearest whole number):
[tex]\begin{gathered} P(8)=3670\cdot0.87^8 \\ \therefore P(8)=1205 \end{gathered}[/tex]