Question

question 1 - 2
izayah 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)=-16t^{2}+64t) would help him find the height 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)

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 average rate of change

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

Answer:

$-16$