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

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) over the interval ([x_1,x_2]) is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}).

Step2: Find the average rate of change between (x_1 = 0.5) and (x_2=2)

From the graph, when (x = 0.5), (y = 2) (assuming the point ((0.5,2))) and when (x = 2), (y = 7) (assuming the point ((2,7))). [ \frac{7 - 2}{2-0.5}=\frac{5}{1.5}=\frac{10}{3}\approx 3.33 ]

Step3: Find the average rate of change between (x_1 = 1.5) and (x_2 = 2.5)

From the graph, when (x=1.5), (y = 6) (assuming the point ((1.5,6))) and when (x = 2.5), (y = 11) (assuming the point ((2.5,11))). [ \frac{11 - 6}{2.5-1.5}=\frac{5}{1}=5 ]

Answer:

The runner's average rate of change between (0.5) and (2) is (\frac{10}{3}\approx 3.33) mph. The runner's average rate of change between (1.5) and (2.5) is (5) mph.