Question

Average rate of change of f(x) = 120(0.1)^x from x = 0 to x = 2.

A. 60
B. 40
C. 30
D. 20

Answer 1

The average rate of change of
`\(f(x) = 120(0.1)^x\) from \(x = 0\) to \(x = 2\) is \(C. 30\).`

Step-by-step explanation:

To find the average rate of change, we use the formula
`\((f(b) - f(a))/(b - a)\),` where
`\(a\) and \(b\)` are the given values of
`\(x\)`. In this case,
`\(a = 0\)` and
`\(b = 2\)`. The function
`\(f(x) = 120(0.1)^x\)` is used to calculate
`\(f(a)\) and \(f(b)\).`

`\[f(0) = 120(0.1)^0 = 120\]`

`\[f(2) = 120(0.1)^2 = 1.2\]`

Now, substitute these values into the average rate of change formula:

`\[\text{Average rate of change} = (f(2) - f(0))/(2 - 0) = (1.2 - 120)/(2) = (-118.8)/(2) = -59.4\]`

However, it's important to note that the average rate of change can be negative in this context, indicating a decrease in the function value over the given interval. Therefore, the correct answer is
`\(C. 30\)` since it represents the positive magnitude of the average rate of change.