8% growth per year, 21,600 in 2012 fox population predicted to be in the year 2020?

Question

The fox population in a certain region has an annual growth rate of 8% per year. In the year 2012, there were 21,600 foxes counted in the area. What is the fox population predicted to be in the year 2020? (Round your answer to the nearest whole number.)

foxes

Answer 1

A growth rate of 8% per year means that at the end of each year, the population is 1.08 times what it was at the start of the year.  Keep this up for t years, starting with an initial population of 21,600 and get

 

P(t) = 21,600 (1.08)^t

 

t = years since 2012, when the population was 21,600

 

For year 2020, 

 

t = 2020 - 2012 = 8

 

P(8) = 21,600 (1.08)⁸ ≅ 39,980