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 =
`(f(5)-f(3))/(5-3) = ((-16( 5^(2))+48(5)+100)-(-16( 3^(2))+48(3)+100 )/(2)=`
`((-16(25)+240+100)-(-16(9)+144+100))/(2) = ((-400+240+100)-(-144+144+100))/(2)=`
`(-60-100)/(2) = (-160)/(2) = -80`