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 give the height of the rocket in feet after t seconds.
what is the average rate of change of the height from 2 seconds to 3 seconds? -16
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 $y = f(x)$ 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 $h(2)$ and $h(3)$

$h(2)=-16\times2^{2}+64\times2=-16\times4 + 128=-64 + 128 = 64$.
$h(3)=-16\times3^{2}+64\times3=-16\times9+192=-144 + 192 = 48$.

Step3: Calculate 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.