Question

question 1-6
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 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

Explanation:

Step1: Find $h(2)$

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

Step2: Find $h(3)$

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

Step3: Calculate average rate of change

The formula for 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, $a = 2$, $b = 3$, $f(t)=h(t)$.
Average rate of change$=\frac{h(3)-h(2)}{3 - 2}=\frac{48 - 64}{1}=-16$.

Answer:

-16