Question

What is the average rate of change of the function f(x)=120(0. 1)x from x = 0 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 is -59.4

The formula for calculating the rate of change of the function is expressed as:

$f'(x)=\frac{f(b)-f(a)}{b-a}$

Given the function

$f(x)=120(0.1)^x\\f(0) = 120(0.1)^0\\f(0)=120$

Get the value of f(2)

$f(2)=120(0.1)^2\\f(2) = 120(0.1)^2\\f(2)=1.2$

Substitute into the formula to have:

$f'(x)=\frac{1.2-120}{2-0}\\f'(x)=\frac{118.8}{2} \\f'(x)= -59.4$

Hence the average rate of change of the function is -59.4

Learn more on the rate of change here: https://brainly.com/question/11627203