# Does linear functions have constant rate of change and exponential functions have constant...

## Question:

Does linear functions have constant rate of change and exponential functions have constant relative rate of change?

## Linear and Exponential Functions:

{eq}\\ {/eq}

The functions of the form {eq}y=ax+b {/eq} i.e. the functions having degree of their variable as unity are known as Linear Functions whereas the functions having constants with power raised on them i.e. {eq}y=e^x {/eq} are termed as Exponential Functions.

## Answer and Explanation:

{eq}\\ {/eq}

We know that Linear functions have the form {eq}y=ax+b {/eq} and on differentiating them, we get a constant, so Linear functions have constant rate of change.

Now, considering the Exponential function {eq}y=e^x {/eq}, the relative rate of change is given by {eq}\dfrac{y'}{y}=\dfrac{e^x}{e^x}=1 {/eq}, which is also constant.

Hence, both statements are true.

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from Explorations in Core Math - Algebra 1: Online Textbook Help

Chapter 9 / Lesson 7