Find the average rate of change of the exponential function f left-parenthesis x right-parenthesis over the interval 1 less-than-or-equal-to x less-than-or-equal-to 3. Values of f left-parenthesis x right-parenthesis are shown in the following table.
x 0 1 2 3 4
f left-parenthesis x right-parenthesis 0.2 1 5 25 125
(1 point)
Responses
6
6
12
12
24
24
start fraction 125 over 3 end fraction
To find the average rate of change of the exponential function over the given interval, we need to find the difference in the values of f(x) at the endpoints of the interval and divide it by the difference in x-values.
The value of f(1) is 1 and the value of f(3) is 25.
Therefore, the average rate of change of the exponential function over the interval 1 ≤ x ≤ 3 is:
(25 - 1) / (3 - 1) = 24 / 2 = 12.
So, the correct answer is 12.