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 =
`(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`