The height of the balloon decreases by an average of 6.875 meters per second from t=7 seconds to t=15 seconds.
How to solve
The average rate of change of function f(t) over the interval [a, b] is calculated as (f(b) - f(a)) / (b - a).
In order to solve for the average rate of change,=
Average rate of change = (h(15) - h(7)) / (15 - 7)
Average rate of change = (20 + 10(15) - 15^2 - (20 + 10(7) - 7^2)) / (15 - 7)
Average rate of change = (170 - 225) / 8
Average rate of change = -55 / 8
Average rate of change = -6.875 meters per second
The height of the balloon decreases by an average of 6.875 meters per second from t=7 seconds to t=15 seconds.
The Complete Question
A helium-filled balloon is released at time t=0 seconds. The height of the balloon in meters above ground is given by the function h(t) = 20 + 10t - t^2, where t is the time in seconds. What is the average rate of change of the balloon's height from t=7 seconds to t=15 seconds?