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

We are given that your weight decreases from 150 pounds at week 0 to 137 pounds at week 5. To find the average rate of change, we use the formula

[tex]$$
\text{Average rate of change} = \frac{\text{Change in weight}}{\text{Change in time}}.
$$[/tex]

First, calculate the change in weight:

[tex]$$
\text{Change in weight} = 137 - 150 = -13 \text{ pounds}.
$$[/tex]

Next, determine the change in time:

[tex]$$
\text{Change in time} = 5 - 0 = 5 \text{ weeks}.
$$[/tex]

Now, substitute these values into the formula:

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

Thus, the average rate of change of your weight over the first five weeks is [tex]$-2.6$[/tex] pounds per week. This corresponds to answer choice d.