You began membership in a new health and fitness club, which provides access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, [tex]w[/tex], as a function of time, [tex]t[/tex], over an eight-week period.

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Time (weeks)} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\text{Weight (lb)} & 150 & 144 & 143 & 141 & 140 & 137 & 137 & 132 & 129 \\
\hline
\end{array}
\][/tex]

If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?

A. +0.38 pounds per week
B. -0.38 pounds per week
C. +2.6 pounds per week
D. -2.6 pounds per week

Please select the best answer from the choices provided.

First, we note that your weight at week 0 is [tex]$150$[/tex] pounds and at week 5 is [tex]$137$[/tex] pounds. This means that the change in weight over the first five weeks is

[tex]$$
\Delta w = 137 - 150 = -13 \text{ pounds}.
$$[/tex]

Since the time interval from week 0 to week 5 is

[tex]$$
\Delta t = 5 \text{ weeks},
$$[/tex]

the average rate of change of weight with respect to time is given by

[tex]$$
\text{Average rate} = \frac{\Delta w}{\Delta t} = \frac{-13}{5} = -2.6 \text{ pounds per week}.
$$[/tex]

Thus, the best answer from the choices is:

d. [tex]$-2.6$[/tex] pounds per week.