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 + 160

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 function that models the height of the ball is:

`f(t)=-16t^2+48t=160`

At t=3,
`f(3)=-16(3)^2+48(3)+160=160`

At t=5,
`f(5)=-16(5)^2+48(5)+160=0`

The average rate of change is simply the slope of the secant line connecting.

`(3,f(3))` and
`(5,f(5))`.

The average rate of change

`=(f(3)-f(5))/(3-5)`

`=(160-0)/(-2)`

`=-80fts^(-1)`