Answer
See the explanation.
Work Step by Step
[Part a]
The slope of a secant line between two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ can be calculated using the formula of rate of change: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
(i) $\frac{7398-3438}{40-0} = 99$ steps/min
(ii) $\frac{5622-4559}{20-10} = 106.3$ steps/min
(iii) $\frac{6536-5622}{30-20} = 91.4$ steps/min
These slops represent the average number of steps she walks between in a specified time interval.
[Part b]
Since 3:20 PM falls inbetween 3:10PM and 3:30 PM, we will take the average of the the slope of secant lines that we calculated in part a for [10,20] and [20,30]
$\frac{106.3+91.4}{2}=98.85$ steps/min
