22\njanelle throws a ball off of a balcony. the given function h models the height, in feet, of the ball t…

22\njanelle throws a ball off of a balcony. the given function h models the height, in feet, of the ball t seconds after it is thrown.\nh(t)= - 16t² + 64t + 80\ncomplete the statement to describe the average rate of change between 2 and 5 seconds.\nthe average rate of change between 2 and 5 seconds is feet per second, showing that the height of the ball is

22\njanelle throws a ball off of a balcony. the given function h models the height, in feet, of the ball t seconds after it is thrown.\nh(t)= - 16t² + 64t + 80\ncomplete the statement to describe the average rate of change between 2 and 5 seconds.\nthe average rate of change between 2 and 5 seconds is feet per second, showing that the height of the ball is

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(t)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 2$, $b = 5$, and $h(t)=-16t^{2}+64t + 80$.

Step2: Calculate $h(2)$

Substitute $t = 2$ into $h(t)$: $h(2)=-16\times2^{2}+64\times2 + 80=-16\times4+128 + 80=-64+128 + 80=144$.

Step3: Calculate $h(5)$

Substitute $t = 5$ into $h(t)$: $h(5)=-16\times5^{2}+64\times5 + 80=-16\times25+320 + 80=-400+320 + 80=0$.

Step4: Calculate the average rate of change

$\frac{h(5)-h(2)}{5 - 2}=\frac{0 - 144}{3}=\frac{-144}{3}=-48$.

Answer:

$-48$