Question

Pleaseeee helpppp me pleaseeeeee

The fox population in a certain region has an annual growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 23600.

(a) Find a function that models the population t 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

Explanation:

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

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

where P0 is the initial population, r is the annual growth rate, and t is the number of years after the initial population.

Plugging in the given values, we get:

P(t) = 23600 * (1 + 0.07)^t

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

P(t) = 23600 * 1.07^t

(b) To estimate the fox population in the year 2008, we need to find the value of P(t) when t = 8 (since 2008 is 8 years after 2000). Plugging in t = 8 into the function from part (a), we get:

P(8) = 23600 * 1.07^8

P(8) ≈ 41333

Therefore, the estimated fox population in the year 2008 is 41,333 (rounded to the nearest integer).