Answer :
To find the average rate of change of weight over the last four weeks of the program (from week 4 to week 8), we'll follow these steps:
1. Identify the data points we need:
- At week 4, the weight is 140 pounds.
- At week 8, the weight is 129 pounds.
2. Calculate the change in weight ([tex]\(\Delta \text{weight}\)[/tex]):
- Subtract the weight at week 4 from the weight at week 8.
[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]\(\Delta \text{time}\)[/tex]):
- Subtract week 4 from week 8.
[tex]\[
\Delta \text{time} = 8 - 4 = 4 \text{ weeks}
\][/tex]
4. Calculate the average rate of change:
- Divide the change in weight by the change in time.
[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]
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 from the choices provided is option a: [tex]\(-2.75\)[/tex] pounds per week.
1. Identify the data points we need:
- At week 4, the weight is 140 pounds.
- At week 8, the weight is 129 pounds.
2. Calculate the change in weight ([tex]\(\Delta \text{weight}\)[/tex]):
- Subtract the weight at week 4 from the weight at week 8.
[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]\(\Delta \text{time}\)[/tex]):
- Subtract week 4 from week 8.
[tex]\[
\Delta \text{time} = 8 - 4 = 4 \text{ weeks}
\][/tex]
4. Calculate the average rate of change:
- Divide the change in weight by the change in time.
[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]
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 from the choices provided is option a: [tex]\(-2.75\)[/tex] pounds per week.
