Question

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

Answer 1

It is growing because the base is greater than 1 and the exponent has a positive sign.

Explanation:

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 `base>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=(1/5)^x`. That's why it is apparently growing but in reality it is decaying.