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

1 Answer
Jun 22, 2015

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


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.