Question

7. The path of a baseball after it has been hit is modeled by the function h = -0.0032d? + d + 3, where his

the height in feet of the baseball and d is the distance in feet the baseball is from home plate. Find the average
rate of change for the baseball between d = 100 and d = 200.

Answer 1

`A = 0.04`

Explanation:

Given

`h(d) = -0.0032d^2 + d + 3`

Required

Determine the average rate of change for d = 100 to 200

Average rate of change (A) is calculated as follows:

`A = (h(b) - h(a))/(b - a)`

In this case:

`b = 200` and
`a = 100`

So:
`A = (h(b) - h(a))/(b - a)` becomes

`A = (h(200) - h(100)/(200 - 100)`

`A = (h(200) - h(100))/(100)`

Solving h(200)

`h(d) = -0.0032d^2 + d + 3`

`h(200) = -0.0032*200^2 + 200 + 3`

`h(200) = 75`

Solving h(100)

`h(d) = -0.0032d^2 + d + 3`

`h(100) = -0.0032*100^2 + 100 + 3`

`h(100) = 71`

So:
`A = (h(200) - h(100))/(100)` becomes

`A = (75 - 71)/(100)`

`A = (4)/(100)`

`A = 0.04`

Hence, the average rate of change is 0.04