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.
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
