The fox population in a certain region has a relative growth rate of 4% per year. It is estimated that the population in year 2000 was 17900.

Question

(A.) Find a function that models the population t years after 2000 (t=0 for 2000)

 

and 

 

(B.) Use the function from part A to estimate the fox population in the year 2008.

------> answer must be an integer.

 

Thanks!

Answer 1

Ashley,

This problem is actually no different than one for interest on a bank account. 4% relative growth means that each year has 4% higher population than the previous year. The general equation is:

 

P_f = P_i(1 + r)^t  where P_f is the final population, P_i is the initial population, r is the annual growth rate in decimal (not %), and t is the time in years.

 

A)    P_f = 17900(1.04)^t

 

B)    P_f = 17900(1.04)⁸ = 24497.386

       Round to the nearest integer   =    24,497 fox in 2008