Question

A gray squirrel population was introduced in a certain region 21 years ago. Biologists observe that the population doubles every seven years, and now the population is 440.

(a) What was the initial squirrel population?
(b) What is the expected squirrel population, P, t years after introduction? P(t)
(c) Estimate the expected squirrel population 10 years from now. (Round your answer to the nearest integer.)

Answer 1

The initial squirrel population was 55. The expected squirrel population, P, after t years is given by the formula P(t) = P0 * 2^(t/7). The estimated squirrel population 10 years from now is 156.

Step-by-step explanation:

(a) Initial population:

Since the squirrel population doubles every seven years, we can use the formula P(t) = P0 * 2t/7, where P0 is the initial population and t is the number of years.

Given that the current population is 440 after 21 years, we can substitute these values into the formula and solve for P0:

440 = P0 * 221/7

440 = P0 * 23

440 = P0 * 8

P0 = 440 / 8

P0 = 55

Therefore, the initial squirrel population was 55.

(b) Expected squirrel population:

The formula P(t) = P0 * 2t/7 gives us the expected squirrel population, P, after t years.

(c) Estimated squirrel population 10 years from now:

To estimate the squirrel population 10 years from now, we can substitute t = 10 into the formula we obtained in part (b):

P(10) = 55 * 210/7

P(10) ≈ 55 * 21.43

P(10) ≈ 55 * 2.8429

P(10) ≈ 156.3569

Since we need to round the answer to the nearest integer, the estimated squirrel population 10 years from now is 156.