Question

What is the average rate of change of the function f(x)=20(1/4)^x from x = 1 to x = 2?

Enter your answer, as a decimal, in the box.

Do not round your answer.

Answer 1

-3.75

Explanation:

The rate of change is defined as the change in f(x) divided by the change in x

rate of change = (f(x2)-f(x1))/(x2-x1)

f(2) = 20 (1/4)^2 = 20 * 1/16 = 20/16 = 5/4

f(1) = 20 * (1/4)^1 = 5

rate of change = (5/4 -5)/(2-1)

Get a common denominator

= (5/4 - 20/4) /1

= -15/4

= -3 3/4

Change to a decimal

= -3.75