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 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]

Using [tex]$\Delta$[/tex] notation, determine the average rate of change of weight over the last four weeks of the program (including weeks 4 and 8 in your calculations).

A. -2.75 pounds per week
B. +2.75 pounds per week
C. -4.0 pounds per week
D. +0.38 pounds per week

Please select the best answer from the choices provided.

To find the average rate of change of weight over the last four weeks of your fitness program, we need to look at your weight at week 4 and week 8. Here's how you can calculate it:

1. Identify the time intervals and weights:
- At week 4, your weight was 140 pounds.
- At week 8, your weight was 129 pounds.

2. Calculate the change in weight ([tex]$\Delta$[/tex] weight):
[tex]\[
\Delta \text{weight} = \text{weight at week 8} - \text{weight at week 4} = 129 - 140 = -11 \text{ pounds}
\][/tex]

3. Calculate the change in time ([tex]$\Delta$[/tex] time):
[tex]\[
\Delta \text{time} = \text{week 8} - \text{week 4} = 8 - 4 = 4 \text{ weeks}
\][/tex]

4. Determine the average rate of change in weight:
[tex]\[
\text{Average rate of change} = \frac{\Delta \text{weight}}{\Delta \text{time}} = \frac{-11 \text{ pounds}}{4 \text{ weeks}} = -2.75 \text{ pounds per week}
\][/tex]

The average rate of change of your weight over the last four weeks is [tex]$-2.75$[/tex] pounds per week.

Therefore, the best answer from the choices provided is:
a. -2.75 pounds per week.