# How do you determine if the equation #y= 5(0.9)^x# represents exponential growth or decay?

##### 1 Answer

Decay.

#### Explanation:

It all depends on the base of the exponential. We divide two cases: if

Otherwise, if

Note that we're not considering negative bases, because

The reason is very simple: if

#(m/n)^2 = (m*m)/(n*n)# #(m/n)^3 = (m*m*m)/(n*n*n)#

And so on. As you can see, the denominator grows faster than the numerator, since

The case