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

Feb 13, 2016

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:

$y = {\left(1.03\right)}^{x}$
graph{1.03^x [-63.5, 277.4, -48.3, 122.2]}

$y = {\left(1.03\right)}^{- x}$
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.