Question

How do you determine if `y=0.2(5)^-x` is an exponential growth or decay?

Answer 1

This is exponential decay. Two ways to tell are discussed below...

Explanation:

First, the negative exponent is an indicator of decay. You could rewrite the expression (without a negative exponent) as

`y=0.2/5^x`

This helps you to see that as `x` gets very large, the expression gets very small - clearly not a case of growth.

Alternatively, you could make a chart in which you test increasing values of `x`, starting at `x=1` (for example) and increasing slowly to `x=5`. You would see the results - the expression would decrease in value rapidly.