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) = −16t^2 + 48t + 100

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

Answer 1

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