Question

question
the function $h(t)=10sqrt{t}$ gives the height in feet of a hot air balloon after $t$ seconds. find the average rate of change from $t = 1$ to $t = 9$.
provide your answer below:

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = H(t)$ from $t=a$ to $t = b$ is $\frac{H(b)-H(a)}{b - a}$. Here, $a = 1$, $b = 9$, and $H(t)=10\sqrt{t}$.

Step2: Calculate $H(9)$ and $H(1)$

$H(9)=10\sqrt{9}=10\times3 = 30$; $H(1)=10\sqrt{1}=10\times1 = 10$.

Step3: Substitute values into formula

$\frac{H(9)-H(1)}{9 - 1}=\frac{30 - 10}{8}=\frac{20}{8}=\frac{5}{2}$.

Answer:

$\frac{5}{2}$