Question

uzayh launched his toy rocket from the ground straight up into the sky with an initial velocity of 64 feet per second. he found the function h(t)= - 16t² + 64t would help him find the rate of change after t seconds. what is the average rate of change of the height from 2 seconds to 3 seconds? interpret the average rate of change when t = 2 to t = 3. the rocket is ascending 16 feet for every 1 second. the rocket is ascending 48 feet for every 1 second. the rocket is descending 16 feet for every 1 second. the rocket is descending 48 feet for every 1 second.

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = h(t)$ from $t = a$ to $t = b$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 2$, $b = 3$, and $h(t)=-16t^{2}+64t$.

Step2: Calculate $h(2)$

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

Step3: Calculate $h(3)$

Substitute $t = 3$ into $h(t)$: $h(3)=-16\times3^{2}+64\times3=-16\times9+192=-144 + 192 = 48$.

Step4: Calculate the average rate of change

$\frac{h(3)-h(2)}{3 - 2}=\frac{48 - 64}{1}=-16$.

Answer:

The rocket is descending 16 feet for every 1 second.