Question

How do you determine if the equation `y=400(1.03)^x` represents exponential growth or decay?

Answer 1

Growth

Explanation:

This is exponential growth. Essentially if the power is positive for `x>0` then it will be exponential growth; if the power is negative for `x>0` then it will be exponential decay.

Here is a graph of the two situations to help you understand them better:

`y=(1.03)^x`
graph{1.03^x [-63.5, 277.4, -48.3, 122.2]}

`y=(1.03)^(-x)`
graph{1.03^(-x) [-160.4, 151.8, -27.7, 128.5]}

Notice that where `x` is positive we a growth and where `x` is negative we have a decay.