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 + 34t + 546

The average rate of change of f(t) from t = 5 seconds to t = 7 seconds is _____ feet per second.

Answer 1

We have the following function:
f(t) = −16t2 + 34t + 546
By definition, the average rate of change is:
Avr = (f (t2) - f (t1)) / (t2 - t1)
We have then:
For t1 = 5:
f (5) = -16*(5)^2 + 34*(5) + 546
f (5) = 316
For t2 = 5:
f (7) = -16*(7)^2 + 34*(7) + 546
f (7) = 0
Substituting values:
Avr = (0 - 316) / (7 - 5)
Avr = -158
Answer:
The average rate of change of f (t) from t = 5 seconds to t = 7 seconds is -158 feet per second.