Find the average rate of change of the exponential function f(x) over the interval 1 less than or equal to x less than or equal to 3 values of f(x) are shown in the following table
X - 0, 1, 2, 3, 4
f(x)- 0.2, 1, 5, 25, 125
To find the average rate of change of the exponential function f(x) over the interval 1 ≤ x ≤ 3, we use the formula:
Average rate of change = (f(3) - f(1)) / (3 - 1)
First, let's find f(3) and f(1) using the given values:
f(3) = 25
f(1) = 1
Plugging these values into the formula, we get:
Average rate of change = (25 - 1) / (3 - 1)
= 24 / 2
= 12
Therefore, the average rate of change of the exponential function f(x) over the interval 1 ≤ x ≤ 3 is 12.