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Answer :
To find the average rate of change of your weight with respect to time over the first five weeks of the program, follow these steps:
1. Identify Initial and Final Weights:
- Initial weight at the start (week 0) is 150 pounds.
- Weight at week 5 is 137 pounds.
2. Calculate Total Weight Loss:
- Subtract the weight at week 5 from the initial weight to determine the total weight lost over the five weeks.
[tex]\[
\text{Weight lost} = 150 \text{ lb} - 137 \text{ lb} = 13 \text{ lb}
\][/tex]
3. Determine the Number of Weeks:
- The time duration is from week 0 to week 5, which is 5 weeks.
4. Calculate the Average Rate of Change:
- The average rate of change of weight with respect to time is found by dividing the total weight lost by the number of weeks.
[tex]\[
\text{Average rate of change} = \frac{\text{Weight lost}}{\text{Number of weeks}} = \frac{13 \text{ lb}}{5 \text{ weeks}} = 2.6 \text{ lb/week}
\][/tex]
5. Determine the Sign of the Rate:
- Since the weight is decreasing over time, the rate of change is negative:
[tex]\[
\text{Average rate of change} = -2.6 \text{ lb/week}
\][/tex]
Thus, the average rate of change of your weight over the first five weeks of the program is [tex]\(-2.6\)[/tex] pounds per week.
The correct answer is d. -2.6 pounds per week.
1. Identify Initial and Final Weights:
- Initial weight at the start (week 0) is 150 pounds.
- Weight at week 5 is 137 pounds.
2. Calculate Total Weight Loss:
- Subtract the weight at week 5 from the initial weight to determine the total weight lost over the five weeks.
[tex]\[
\text{Weight lost} = 150 \text{ lb} - 137 \text{ lb} = 13 \text{ lb}
\][/tex]
3. Determine the Number of Weeks:
- The time duration is from week 0 to week 5, which is 5 weeks.
4. Calculate the Average Rate of Change:
- The average rate of change of weight with respect to time is found by dividing the total weight lost by the number of weeks.
[tex]\[
\text{Average rate of change} = \frac{\text{Weight lost}}{\text{Number of weeks}} = \frac{13 \text{ lb}}{5 \text{ weeks}} = 2.6 \text{ lb/week}
\][/tex]
5. Determine the Sign of the Rate:
- Since the weight is decreasing over time, the rate of change is negative:
[tex]\[
\text{Average rate of change} = -2.6 \text{ lb/week}
\][/tex]
Thus, the average rate of change of your weight over the first five weeks of the program is [tex]\(-2.6\)[/tex] pounds per week.
The correct answer is d. -2.6 pounds per week.
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