Answer: The average rate of change over the interval 12 < x < 30 is -4/3
Explanation:
The average rate of change over an interval is defined as the change in the output (f(x)) divided by the change in the input (x) over that interval. In this case, the interval is 12 < x < 30. To find the average rate of change, we need to evaluate the function at the endpoints of the interval and subtract the value at the start point from the value at the end point, and divide that by the change in x.
Given the table:
f(30) = 16 and f(12) = 40
The average rate of change over the interval 12 < x < 30 is:
(f(30) - f(12)) / (30 - 12) = (16 - 40) / 18 = -24/18 = -4/3
So the average rate of change over the interval 12 < x < 30 is -4/3
It's worth noting that this is only the average rate of change, and the function may have different rates of change at different points within the interval 12 < x < 30.