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

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-3.75

Step-by-step 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