Question

A population of butterflies decreases exponentially at a rate of 18.3% per year.

What is the equivalent monthly rate to the nearest hundredth of a percent?

1.27%
1.41%
1.53%
1.67%

Answer 1

1.67

Explanation:

Answer 2

The population of butterflies decreases exponentially at a rate of 18.3% per year which equal to 18.3% per 12 month. The exponent function will look like:
an=a0(1+r)^t

If you want to convert year into the month, it is like convert t into 12 t. The calculation would be:
a0(1+r1)^t = a0(1+r2)^12t
(1-0.183)^1 = (1+r2)^12
(0.817) = (1+r2)^12

`\sqrt[12]{0.817}` = (1+r2)^(12/12)
1+r2= 0.983298
r2= 0.98329-1= 0.01671= 1.67%