Question

The fox population in a certain region has an annual growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 23700.

(a) Find a function that models the population
years after 2000 (
for 2000).
Your answer is



(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

(a) To find a function that models the fox population years after 2000, we can use the formula for exponential growth:

P(t) = P0 * (1 + r)^t

Where:
P(t) represents the population at time t
P0 represents the initial population (in the year 2000)
r represents the annual growth rate (4% or 0.04)
t represents the number of years after 2000

So, the function that models the fox population years after 2000 is:

P(t) = 23700 * (1 + 0.04)^t

(b) To estimate the fox population in the year 2008, we substitute t = 8 into the function:

P(8) = 23700 * (1 + 0.04)^8
P(8) = 23700 * (1.04)^8
P(8) ≈ 23700 * 1.3605
P(8) ≈ 32201

Therefore, the estimated fox population in the year 2008 is approximately 32,201.