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 + 160

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

Answer 1

Answer:

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is -80 feet per second.

Step-by-step explanation:

The function that models the height of the ball is:

$f(t)=-16t^2+48t=160$

At t=3, $f(3)=-16(3)^2+48(3)+160=160$

At t=5, $f(5)=-16(5)^2+48(5)+160=0$

The average rate of change is simply the slope of the secant line connecting.

$(3,f(3))$ and $(5,f(5))$.

The average rate of change

$=\frac{f(3)-f(5)}{3-5}$

$=\frac{160-0}{-2}$

$=-80fts^{-1}$