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(

Question

9 days ago

13

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 + 32t + 384

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

Mathematics

2 answers:

Zina [11.9K] · Answer 1 · 2026-03-31T20:20:17+03:00

Zina [11.9K]9 days ago

6 0

The response for the blank is simply -128.

Zina [11.9K] · Answer 2 · 2026-03-31T20:19:42+03:00

In this situation, we consider the following function: f(t) = -16t² + 32t + 384. To determine the average rate of change, we utilize the formula: AVR = (f(t2) - f(t1)) / (t2 - t1). Here, for t1 = 4, we calculate f(4) = -16 * (4)² + 32 * (4) + 384, which yields f(4) = 256. For t2 = 6, f(6) = -16 * (6)² + 32 * (6) + 384 results in f(6) = 0. Plugging these values into the average rate of change formula gives us AVR = (0 - 256) / (6 - 4), simplifying to AVR = -128. Therefore, the average rate of change of f(t) from t = 4 seconds to t = 6 seconds is -128 feet per second.