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+32t+90
The average rate of change of f(t) from t=4 seconds to t=6 seconds is______ feet per second .

Answer 1

It is given that f(t) = -16t² + 32t + 90
The average rate of change will be calculated as following

$rate \ of \ change = \frac{f( t_{2})-f( t_{1})}{ t_{2} - t_{1}}$

At t₁ = 4 ⇒⇒⇒ f(t₁) = -16*(4)² + 32*(4) + 90 = -38
At t₂ = 6 ⇒⇒⇒ f(t₂) = -16*(6)² + 32*(6) + 90 = -294

∴ $rate \ of \ change = \frac{(-294)-(-38)}{6-4}= \frac{-256}{2}=-128\ ft/sec.$

So, The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is 128 feet per second .