Question

A study of the annual population of butterflies in a county park shows the population, B(t), can be represented by the function B(t)=137(1.085)t, where the t represents the number of years since the study started. Based on the function, what is the growth rate?

Answer 1

The growth rate is of 0.085 = 8.5% a year.

Explanation:

General growth equation:

`B(t) = B(0)(1+r)^(t)`

In which B(t) is the population of butterflies after t years, B(0) is the initial population and r is the growth rate, as a decimal.

We have:

`B(t)=137(1.085)^(t)`

Comparing to the general equation, we have that:

`B(0) = 137, 1 + r = 1.085`

Growh rate:

1 + r = 1.085

r = 1.085 - 1

r = 0.085

The growth rate is of 0.085 = 8.5% a year.