growth/ decay percentage

Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y = 68(1.038)^x

Answer 1

General formula for an exponential:

y = a·b^x

where b = 1 + rate and the rate is expressed as a decimal. It's growth if rate > 0 and decay if the rate < 0. In the problem, b = 1.038:

1.038 = 1 + rate

Solve for rate and determine if it's growth or decay. Multiply rate by 100 to convert to a percent.