the function $h(t)=-2t^{2}+30t + 50$ represents the number of customers that enter a mall at time $t$ hours…

the function $h(t)=-2t^{2}+30t + 50$ represents the number of customers that enter a mall at time $t$ hours. what is the average rate of change of the number of customers over the interval $1leq tleq3$? the average rate of change is 38, which means the number of customers increases by an average of 38 each hour from the 1st until the 3rd hour. the average rate of change is 22, which means the number of customers increases by an average of 22 each hour from the 1st until the 3rd hour. the average rate of change is 44, which means the number of customers increases by an average of 44 each hour from the 1st until the 3rd hour. the average rate of change is 50, which means the number of customers increases by an average of 50 each hour from the 1st until the 3rd hour.

the function $h(t)=-2t^{2}+30t + 50$ represents the number of customers that enter a mall at time $t$ hours. what is the average rate of change of the number of customers over the interval $1leq tleq3$? the average rate of change is 38, which means the number of customers increases by an average of 38 each hour from the 1st until the 3rd hour. the average rate of change is 22, which means the number of customers increases by an average of 22 each hour from the 1st until the 3rd hour. the average rate of change is 44, which means the number of customers increases by an average of 44 each hour from the 1st until the 3rd hour. the average rate of change is 50, which means the number of customers increases by an average of 50 each hour from the 1st until the 3rd hour.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(t)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 1$, $b = 3$, and $h(t)=-2t^{2}+30t + 50$.

Step2: Calculate $h(3)$

Substitute $t = 3$ into $h(t)$: $h(3)=-2(3)^{2}+30(3)+50=-2\times9 + 90+50=-18 + 90+50=122$.

Step3: Calculate $h(1)$

Substitute $t = 1$ into $h(t)$: $h(1)=-2(1)^{2}+30(1)+50=-2 + 30+50=78$.

Step4: Calculate the average rate of change

$\frac{h(3)-h(1)}{3 - 1}=\frac{122 - 78}{2}=\frac{44}{2}=22$.

Answer:

The average rate of change is 22, which means the number of customers increases by an average of 22 each hour from the 1st until the 3rd hour.