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 + 100The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

Answer 1

For this case we have the following function:
f (t) = -16t2 + 48t + 100
The average rate of change is:
(f (t2) - f (t1)) / (t2 - t1)
We have then:
For t1 = 3:
f (3) = -16 * (3) ^ 2 + 48 * (3) + 100
f (3) = 100
For t2 = 5:
f (5) = -16 * (5) ^ 2 + 48 * (5) + 100
f (5) = -60
Substituting values:
AVR = (-60 - 100) / (5 - 3)
AVR = -80
Answer:
The average rate of change of f (t) from t = 3 seconds to t = 5 seconds is -80 feet per second.