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Answer :
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
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
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