Question

Help me please :(

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 27500.

(a) Find a function that models the population t years after 2000 (t=0 for 2000).
Hint: Use an exponential function with base e.
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

Explanation:

(a) To model the population t years after 2000 with an annual growth rate of 8 percent per year, we can use the formula for exponential growth:

P(t) = P0 * e^(rt)

where P0 is the initial population, r is the annual growth rate as a decimal, and t is the time in years.

Given that the initial population in the year 2000 was 27500 and the annual growth rate is 8 percent, we have:

P0 = 27500

r = 0.08

Using e as the base of the exponential function, the function that models the fox population t years after 2000 is:

P(t) = 27500 * e^(0.08t)

(b) To estimate the fox population in the year 2008, we need to substitute t = 8 in the function obtained in part (a):

P(8) = 27500 * e^(0.08*8)

P(8) = 27500 * e^(0.64)

P(8) ≈ 54122

Therefore, the estimated fox population in the year 2008 is approximately 54122.