Question

A population of 40 foxes in a wildlife preserve doubles in size every 15 years. The function y=40•2*, where x is the number of 15 years periods, models the population growth. How many foxes will there be after 30 years?

Answer 1

There will be 160 foxes after 30 years.

Explanation:

If the population of 40 foxes doubles every 15 years, then after 15 years (one period) it will be 2 times the initial population (240 = 80), and after 30 years (two periods) it will be 2 times the population after 15 years, which is 280 = 160.

Using the given function, we can also plug in x = 2 (since 30 years is two 15-year periods) and solve for y:

y = 40 * 2^2

y = 40 * 4

y = 160

Therefore, there will be 160 foxes after 30 years.