Question

Calculate the average rate of change over the interval [1, 3] for the following function.

f(x)=4(5)^x

A. -260
B. 260
C. 240
D. -240

Answer 1

The correct answer is C,240

Explanation:

we cannot see the function, and do not know it's coordinates, we can set the value of x equal to 1, and then 3, and use the coordinate pairs to solve for the rate of change (slope).

4(5)^1

4(5)

20

Our first coordinate pair is 1, 20.

4(5)^3

4(125)

500

Our second coordinate pair is 3, 500.

Now, apply the slope formula:

500 - 20 / 3 - 1

480 / 2

Answer 2

Because we cannot see the function, and do not know it's coordinates, we can set the value of x equal to 1, and then 3, and use the coordinate pairs to solve for the rate of change (slope).

4(5)^1

4(5)

20

Our first coordinate pair is 1, 20.

4(5)^3

4(125)

500

Our second coordinate pair is 3, 500.

Now, apply the slope formula:

`(y.2 - y.1)/(x.2 - x.1) = m`

500 - 20 / 3 - 1

480 / 2

240

The correct answer is C, or 240.