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, ft, in feet, at different times t in seconds:

f(t) = -16t2 + 32t + 90

The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is _____ feet per second.

Answer 1

Hey, just a question before I attempt to explain how to do this for you. Have you taken calculus or general physics? Do you know the average value formula?

Answer 2

No.

Answer 3

In that case, the rate of change is just the slope between the value of f(t) at 4 seconds and the value of f(t) at 6 seconds.

Think of the seconds as the x-axis and f(t) as the y-axis. You know that a slope is:
\[\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }\]

In this case, your \[y_{2} = f(6 seconds)\]
and your
\[y_{1} = f(4 seconds)\]

Your
\[x_{2} = 6 seconds\]
and your
\[x_{1} = 4 seconds\]

Does that help?