# Determine whether the function represents exponential growth or exponential decay. Then identify the percent rate of change. y=5(0.6)^t

Question
Exponential growth and decay
Determine whether the function represents exponential growth or exponential decay. Then identify the percent rate of change. y=5(0.6)^t

2020-12-06
If the base of the exponential function is smaller than 1, then the function represents exponential decay. If the base is greater than 1, then the function represents exponential growth.
For this function we note that the base is 0.6(< 1) and thus the function represents exponential decay.
The percentage rate of change is the (positive) difference between 100% and the base:
$$\displaystyle{\left|{100}\%-{0.6}\right|}={\left|{100}\%-{60}\%\right|}={40}\%$$

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