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Answer :
To determine the average rate of change of weight over the last four weeks of the program, we will use [tex]$\Delta$[/tex] notation. The average rate of change formula is as follows:
[tex]\[
\text{Average rate of change} = \frac{\Delta w}{\Delta t} = \frac{w_{\text{final}} - w_{\text{initial}}}{t_{\text{final}} - t_{\text{initial}}}
\][/tex]
Here, we are interested in the change from week 4 to week 8.
1. Identify the weights at week 4 and week 8:
- Weight at week 4: [tex]\( w_4 = 140 \)[/tex]
- Weight at week 8: [tex]\( w_8 = 129 \)[/tex]
2. Identify the corresponding times:
- Initial time, [tex]\( t_{\text{initial}} = 4 \)[/tex]
- Final time, [tex]\( t_{\text{final}} = 8 \)[/tex]
3. Calculate the change in weight ([tex]\(\Delta w\)[/tex]):
[tex]\[
\Delta w = w_8 - w_4 = 129 - 140 = -11 \text{ pounds}
\][/tex]
4. Calculate the change in time ([tex]\(\Delta t\)[/tex]):
[tex]\[
\Delta t = t_{\text{final}} - t_{\text{initial}} = 8 - 4 = 4 \text{ weeks}
\][/tex]
5. Calculate the average rate of change of weight:
[tex]\[
\text{Average rate of change} = \frac{\Delta w}{\Delta t} = \frac{-11}{4} = -2.75 \text{ pounds per week}
\][/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 best answer from the choices provided is:
a. -2.75 pounds per week
[tex]\[
\text{Average rate of change} = \frac{\Delta w}{\Delta t} = \frac{w_{\text{final}} - w_{\text{initial}}}{t_{\text{final}} - t_{\text{initial}}}
\][/tex]
Here, we are interested in the change from week 4 to week 8.
1. Identify the weights at week 4 and week 8:
- Weight at week 4: [tex]\( w_4 = 140 \)[/tex]
- Weight at week 8: [tex]\( w_8 = 129 \)[/tex]
2. Identify the corresponding times:
- Initial time, [tex]\( t_{\text{initial}} = 4 \)[/tex]
- Final time, [tex]\( t_{\text{final}} = 8 \)[/tex]
3. Calculate the change in weight ([tex]\(\Delta w\)[/tex]):
[tex]\[
\Delta w = w_8 - w_4 = 129 - 140 = -11 \text{ pounds}
\][/tex]
4. Calculate the change in time ([tex]\(\Delta t\)[/tex]):
[tex]\[
\Delta t = t_{\text{final}} - t_{\text{initial}} = 8 - 4 = 4 \text{ weeks}
\][/tex]
5. Calculate the average rate of change of weight:
[tex]\[
\text{Average rate of change} = \frac{\Delta w}{\Delta t} = \frac{-11}{4} = -2.75 \text{ pounds per week}
\][/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 best answer from the choices provided is:
a. -2.75 pounds per week
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