After years of overhunting, environmental scientists have reintroduced wolverines to Yellowstone National Park. The initial number of wolverines reintroduced to the park was 88 and, after 5 years, the population is estimated to be around 578. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new wolverine population in Yellowstone National Park?

Hint: A(t) = A0(1 + r)t, where A(t) is the final amount, A0 is the initial amount, r is the growth rate expressed as a decimal amount, and t is time.

Question

After years of overhunting, environmental scientists have reintroduced wolverines to Yellowstone National Park. The initial number of wolverines reintroduced to the park was 88 and, after 5 years, the population is estimated to be around 578. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new wolverine population in Yellowstone National Park?

Hint: A(t) = A0(1 + r)t, where A(t) is the final amount, A0 is the initial amount, r is the growth rate expressed as a decimal amount, and t is time.

Vocaloid · Answer

A(t) = A0(1+r)^t be careful with the exponent

A0 = initial population 
A(t) = the population after five years
t = time = five years

Solve for r