Question

Please if you really know how to to this 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

(a) The exponential growth model for the fox population can be represented as:

P(t) = P(0) * e^(rt)

where P(0) is the initial population, r is the annual growth rate as a decimal, t is the time in years.

Plugging in the given values, we get:

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

Therefore, 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 find t = 8 (since 2008 is 8 years after 2000). Plugging in t = 8 in the function from part (a), we get:

P(8) = 27500 * e^(0.08*8) = 27500 * e^0.64

P(8) ≈ 57,012

Therefore, the estimated fox population in the year 2008 is 57,012 (rounded to the nearest integer).