# How do you determine if the equation y = 5^x represents exponential growth or decay?

First of all $y = {5}^{x}$ it's not only an equation, but it's also a function called "Exponential function". The base (5 in this case) determine the growth or decay of the function. If $b a s e > 1$ then the function grows, otherwise if base is between 0 and 1, the function decays. We assume that the base is positive and it's not 1 or 0.
Another thing to notice is that if you have $y = {5}^{- x}$ this function could be rewritten in this way: $y = {\left(\frac{1}{5}\right)}^{x}$. That's why it is apparently growing but in reality it is decaying.