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Answer :
To find the average rate of change of weight with respect to time over the first five weeks, you need to calculate how much weight was lost per week on average. Here's how you can do it step by step:
1. Identify the Initial Weight and Final Weight:
- At week 0, the initial weight was 150 pounds.
- At week 5, the weight was 137 pounds.
2. Determine the Total Weight Lost:
- Subtract the weight at week 5 from the initial weight:
[tex]\[
\text{Weight Lost} = 150\, \text{pounds} - 137\, \text{pounds} = 13\, \text{pounds}
\][/tex]
3. Calculate the Average Rate of Change:
- The formula for the average rate of change is:
[tex]\[
\text{Average Rate of Change} = \frac{\text{Total Weight Lost}}{\text{Number of Weeks}}
\][/tex]
- Here, the total weight lost is 13 pounds, and the period is 5 weeks, so:
[tex]\[
\text{Average Rate of Change} = \frac{13}{5} = 2.6\, \text{pounds per week}
\][/tex]
4. Determine the Sign of the Rate of Change:
- Since the weight decreased over the 5 weeks, the average rate of change is negative, indicating a loss:
[tex]\[
\text{Average Rate of Change} = -2.6\, \text{pounds per week}
\][/tex]
Thus, the best answer among the choices provided is d. -2.6 pounds per week.
1. Identify the Initial Weight and Final Weight:
- At week 0, the initial weight was 150 pounds.
- At week 5, the weight was 137 pounds.
2. Determine the Total Weight Lost:
- Subtract the weight at week 5 from the initial weight:
[tex]\[
\text{Weight Lost} = 150\, \text{pounds} - 137\, \text{pounds} = 13\, \text{pounds}
\][/tex]
3. Calculate the Average Rate of Change:
- The formula for the average rate of change is:
[tex]\[
\text{Average Rate of Change} = \frac{\text{Total Weight Lost}}{\text{Number of Weeks}}
\][/tex]
- Here, the total weight lost is 13 pounds, and the period is 5 weeks, so:
[tex]\[
\text{Average Rate of Change} = \frac{13}{5} = 2.6\, \text{pounds per week}
\][/tex]
4. Determine the Sign of the Rate of Change:
- Since the weight decreased over the 5 weeks, the average rate of change is negative, indicating a loss:
[tex]\[
\text{Average Rate of Change} = -2.6\, \text{pounds per week}
\][/tex]
Thus, the best answer among the choices provided is d. -2.6 pounds per week.
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