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

$f(t) = -16t^{2} +48t + 100$
Average rate of change from t = 3 seconds to t = 5 seconds = $\frac{f(5)-f(3)}{5-3} = \frac{(-16( 5^{2})+48(5)+100)-(-16( 3^{2})+48(3)+100 }{2}=$$\frac{(-16(25)+240+100)-(-16(9)+144+100)}{2} = \frac{(-400+240+100)-(-144+144+100)}{2}=$ $\frac{-60-100}{2} = \frac{-160}{2} = -80$