what is the runners average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph done speed of…

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, $y$ is the miles run and $x$ is the time in hours.

Step2: Calculate average rate of change for the interval $[0.5,2]$

From the graph, when $x = 0.5$, $y\approx3$ and when $x = 2$, $y = 10$. The average rate of change is $\frac{10 - 3}{2-0.5}=\frac{7}{1.5}=\frac{7}{\frac{3}{2}}=\frac{14}{3}\approx4.67$ mph.

Step3: Calculate average rate of change for the interval $[1.5,2.5]$

From the graph, when $x = 1.5$, $y\approx8$ and when $x = 2.5$, $y = 12$. The average rate of change is $\frac{12 - 8}{2.5 - 1.5}=\frac{4}{1}=4$ mph.

Answer:

4.67 mph 4 mph