Question

The fox population in a certain region has a continuous growth rate of 5 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) (b) Use the function from part (a) to estimate the fox population in the year 2008.

Answer 1

This problem is actually no different than one for interest on a bank account. 5% relative growth means that each year has 5% 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 = 23600(1.05)^t

B)    P_f = 23600(1.04)⁸ = 32298.23

       Round to the nearest integer   = 32298 fox in 2008

Hope This Helps!