Question

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 100 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

Answer 1

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is __-80___feet per second.

Explanation:

The average change rate m is calculated using the following formula

`m=(f(t_2)-f(t_1))/(t_2-t_1)`

In this case
`f(t) = -16t^2 + 48t + 100`,
`t_2 = 5\ s\ \ , t_1=3\ s`

Then

`f(t_2) = f(5) =-16(5)^2 + 48(5) + 100`

`f(t_2) = -60`

`f(t_1) = f(3) =-16(3)^2 + 48(3) + 100`

`f(t_1) = 100`

Finally

`m=((-60)-100)/(5-3)`

`m=-80`