The average rate of change of height is speed.
The average rate of change of d(t) on t ∈ [2, 5] represents the ball's average speed over that interval of time.
Answer
Find out what does the average rate of change of d(t) from t = 2 to t = 5 represent .
To prove
Formula
[tex]Average\ rate\ of\ change = \frac{d(5) - d(2)}{change\ in\ time}[/tex]
As given
The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t²
where d equals the distance traveled at time t seconds .
Now
d(5) = 16 × 5 × 5
= 400 feet
d(2) = 16 × 2 × 2
= 64 feet
Now
Change in time = 5 - 2
= 3 second
put all the values in the above formula
[tex]Average\ rate\ of\ change = \frac{400 - 64}{3}[/tex]
[tex]Average\ rate\ of\ change = \frac{336}{3}[/tex]
Average rate of change is 112 feet/second.
