Question

What is the average rate of change of the functionf(x)=20(14)x from x = 1 to x = 2? enter your answer, as a decimal, in the box. do not round your answer.

Answer 1

The average rate of change of the function f(x) is found as  -3.75.

Explain the term average rate of change?

• The rate about which one value in a function evolves in proportion to another is known as the average rate of change.
• The slope of a graphical representation function is typically calculated using the average rate of change.

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

A(x) = f(b) - f(a) / b - a

The function being:

f(x) = 20.(1/4)ˣ

Its average rate of change between x = 1 to x = 2 must be determined.

At x = 1

Then;

f(x) = 20.(1/4)¹

f(1) = 5

At x = 2

Then;

f(x) = 20.(1/4)²

f(2) = 1.25

Add these to the formula above to get;

A(x) = f(2) - f(1) / 2 - 1

A(x) = - 3.75

Consequently, the average rate of change of a function f(x) between x = 1 and x = 2 is -3.75.

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