Question

The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 26600(a) Find a function that models the population years after 2000(t = 0 for 2000) . Your answer is P(t) =( b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer should be an integer)

Answer 1

Step-by-step explanation

In this problem, we have a model for the fox population in a certain region. We know that:

• the population has an annual growth rate of 8% per year, so the ratio is r = 0.08,

,

• the estimated population in the year 2000 was P(0) = 26,600.

We must find a function of the population as a function of time t (in years), starting with t = 0 at the year 2000.

(1) The population is given by the exponential function:

`P(t)=P_0\cdot(1+r)^t.`

Replacing the data from above, we get:

`P(t)=26,600\cdot(1+0.08)^t=26,600\cdot1.08^t.`

(2) At year 2008, we have t = 2008 - 2000 = 8. Replacing this value in the formula above, we get:

`P(8)=26,600\cdot1.08^8\cong49,235.`Answer

(a) P(t) = 26,600*1.08^t

`P(t)=26,600\cdot1.08^t`

(b) 49,235