Question

Dr. Lynch is studying an endangered fox whose population is declining by 13% every year. If there are currently 3,670 foxes, how many will remain in 8 years?If necessary, round your answer to the nearest whole number.

Answer 1

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:

`P(t)=A\cdot b^t`

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:

`\begin{gathered} A=3670 \\ b=0.87 \end{gathered}`

The final model is:

`P(t)=3670\cdot0.87^t`

After 8 years (t = 8), the population will be (to the nearest whole number):

`\begin{gathered} P(8)=3670\cdot0.87^8 \\ \therefore P(8)=1205 \end{gathered}`