Question

Consider the graph of f(x) = 5x + 1. Explain how to find the average rate of change between x = 0 and x = 4.

What is the average rate of change?

Answer 1

Given:

Consider the given function is:

`f(x)=5^x+1`

To find:

The average rate of change between x = 0 and x = 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

`m=(f(b)-f(a))/(b-a)`

We have,

`f(x)=5^x+1`

At
`x=0`,

`f(0)=5^0+1`

`f(0)=1+1`

`f(0)=2`

At
`x=0`,

`f(4)=5^4+1`

`f(4)=625+1`

`f(4)=626`

Now, the average rate of change between x = 0 and x = 4 is:

`m=(f(4)-f(0))/(4-0)`

`m=(626-2)/(4)`

`m=(624)/(4)`

`m=156`

Hence, the average rate of change between x = 0 and x = 4 is 156.