Chapter 2.1, Problem 2E

A student bought a smartwatch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded $t$ minutes after 3:00 PM on the first day she wore the watch.

(a) Find the slopes of the secant lines corresponding to the given intervals of $t$ . What do these slopes represent?

(i) $\left[0,40\right]$

(ii) $\left[10,20\right]$

(iii) $\left[20,30\right]$

(b) Estimate the student's walking pace, in steps per minute, at 3: 20 PM by averaging the slopes of two secant lines.