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

Given that a ball which has been thrown up can be modeled by the function:
f(t)=-16t^2+48t+100
the rate of change will be:
f'(t)=-32t+48
thus:
when t=3
f(3)=-32(3)+48=-48

when t=5
f(5)=-32(5)+48=-112
thus the rate of change will be:
[f(5)-f(3)]/(5-3)
=(-112-(-48))/(5-3)
=(-64/2)
=-32 ft/sec