Find the average rate of change of the exponential function f(x) over the interval 1≤x≤3. Values of f(x) are shown in the following table.
x f(x)
0 0.2
1 1
2 5
3 25
4 125
a. 6
b. 12
c. 24
d. 125/3
To find the average rate of change of the exponential function f(x) over the interval 1≤x≤3, we need to calculate the change in f(x) divided by the change in x.
The change in f(x) from x=1 to x=3 is f(3) - f(1) = 25 - 1 = 24.
The change in x from x=1 to x=3 is 3 - 1 = 2.
Therefore, the average rate of change is 24/2 = 12.
The answer is: b. 12.