# How do you tell whether #f(x)=(6/5)^-x# is an exponential growth or decay?

##### 2 Answers

Given the form

If

If

#### Explanation:

To understand why this makes sense, let's expand the function that is given. To do this, we need to keep in mind two properties of exponents:

First,

Second,

Using the first property, expand the equation given in the problem:

Now, use the second property to flip the fraction and drop the negative sign from the exponent:

Now that we've gotten this far, let's consider what will happen to the value of

Graph of

graph{5^x [-5, 5, -1.47, 5]}

Graph of

graph{6^x[-5, 5, -1.47, 5]}

Looking at the difference between these two graphs,

If

Decay

#### Explanation:

Given:

Set as:

The index (power) being negative is another way of writing:

This is the same as:

As

Thus the whole will become less and less as

Thus we have

And

Thus it is decay