Question

19.53 38.47|63.5 | 94

| 12
What is the average rate of change in the area
the radius changes from 25 to 5.5 feet?​

Answer 1

95.85

Explanation:

The area A of a circle as a function of its radius r is given by πr².

So, A(r) = πr²

Now, if there is a function f(x) and we have to calculate the average rate of change between the interval x = a and x = b is given by

`(f(b) - f(a))/(b - a)`

Now, A(5.5) = π(5.5)² = 95.07 and A(25) = π(25)² = 1964.28

So, the average rate of change in area between the intervals r = 5.5 to r = 25 will be given by

`(A(25) - A(5.5))/(25 - 5.5) = (1964.28 - 95.07)/(25 - 5.5) = 95.85` (Answer)