Question

average rate of change practice
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tyler is an engineer and needs to design a rocket for an experiment. he has calculated that the height of the rocket, in feet, with respect to time, in seconds, can be modeled by the function h(t)= - 16t² + 160t. find the average rate of change of the rocket over the interval 4,8. (1 point)
the average rate of change is feet per second
check answer remaining attempts: 3

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$, $b = 5$ and $h(t)=-16t^{2}+160t$.

Step2: Calculate $h(4)$

Substitute $t = 4$ into $h(t)$:
$h(4)=-16\times4^{2}+160\times4=-16\times16 + 640=-256+640 = 384$.

Step3: Calculate $h(5)$

Substitute $t = 5$ into $h(t)$:
$h(5)=-16\times5^{2}+160\times5=-16\times25+800=-400 + 800=400$.

Step4: Calculate average rate of change

Use the formula $\frac{h(5)-h(4)}{5 - 4}$.
$\frac{400 - 384}{5 - 4}=\frac{16}{1}=16$.

Answer:

16