what is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph done

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 $\frac{f(b)-f(a)}{b - a}$.

Step2: For the interval $[0.5,2]$

From the graph, when $x = 0.5$, $y\approx3$ and when $x = 2$, $y\approx7$. Then the average rate of change is $\frac{7 - 3}{2-0.5}=\frac{4}{1.5}=\frac{8}{3}\approx2.67$ mph.

Step3: For the interval $[1.5,2.5]$

When $x = 1.5$, $y\approx8$ and when $x = 2.5$, $y\approx11$. Then the average rate of change is $\frac{11 - 8}{2.5 - 1.5}=\frac{3}{1}=3$ mph.

Answer:

For the interval $0.5$ and $2$: $\frac{8}{3}$ mph For the interval $1.5$ and $2.5$: $3$ mph