Question

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 rate 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 descending 0 -16 -48 16 48 every 1 second

Explanation:

Step1: Recall average - rate - of - change formula

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

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

Using the formula $\frac{h(3)-h(2)}{3 - 2}$, we have $\frac{48 - 64}{1}=\frac{-16}{1}=-16$.

Answer:

-16