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]

Using [tex]\Delta[/tex] notation, determine the average rate of change of weight over the last four weeks of the program (include 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 the program (including weeks 4 and 8), we can follow these steps:

1. Identify the Relevant Data Points:
- Weight at week 4: 140 lbs
- Weight at week 8: 129 lbs

2. Determine the Time Duration:
- You are looking at the period from week 4 to week 8.
- This is a duration of [tex]$ 8 - 4 = 4 $[/tex] weeks.

3. Calculate the Change in Weight ([tex]$\Delta w$[/tex]):
- The change in weight is the final weight minus the initial weight.
- [tex]$\Delta w = 129 \text{ lbs} - 140 \text{ lbs} = -11 \text{ lbs}$[/tex]

4. Calculate the Average Rate of Change:
- The average rate of change is the change in weight divided by the time duration.
- [tex]$\frac{\Delta w}{\Delta t} = \frac{-11 \text{ lbs}}{4 \text{ weeks}} = -2.75 \text{ pounds per week}$[/tex]

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

The correct answer is:
a. -2.75 pounds per week