Question

What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?

Answer 1

37.5

Explanation:

5(2)^x = 5(2)^1 = 10

5(2)^x = 5(2)^5 = 160

160 - 10 = 150

5 - 1 = 4

150/4 = 37.5

Answer 2

Average rate of change refers to the slope of a function/equation.
To solve this, plug in for both x values and calculate the average, or mean.

x = 1
f(1) = 5(2)^1
= 5(2)
= 10

x = 5
f(5) = 5(2)^5
= 5(32)
= 160

Now, you calculate the average:
10 + 160 = 170
Divide by 2 and you get 85.