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Answer :
To solve the problem, we need to find the ratio of the change in weight to the change in time for the first five weeks and interpret what this ratio means.
Step 1: Identify the initial data.
For the first five weeks, we have the following data:
- Initial weight at week 0 = 150 pounds
- Weight at week 5 = 137 pounds
Step 2: Calculate the change in weight.
The change in weight is calculated by subtracting the weight at week 5 from the initial weight:
Change in weight = Initial weight - Weight at week 5
Change in weight = 150 pounds - 137 pounds
Change in weight = 13 pounds
This indicates a loss of 13 pounds over the first five weeks.
Step 3: Calculate the change in time.
Since we are considering the first five weeks:
Change in time = Week 5 - Week 0
Change in time = 5 weeks - 0 weeks
Change in time = 5 weeks
Step 4: Formulate the ratio.
The ratio of the change in weight to the change in time is:
[tex]\[
\text{Ratio} = \frac{\text{Change in weight}}{\text{Change in time}} = \frac{13 \text{ pounds}}{5 \text{ weeks}}
\][/tex]
Step 5: Interpret the result.
The ratio [tex]\(\frac{-13}{5}\)[/tex] indicates that 13 pounds were lost over 5 weeks. This means that, on average, you lost [tex]\(2.6\)[/tex] pounds per week. Therefore, the correct interpretation is:
c. [tex]\(-\frac{13}{5}\)[/tex], 13 pounds was lost in 5 weeks.
Step 1: Identify the initial data.
For the first five weeks, we have the following data:
- Initial weight at week 0 = 150 pounds
- Weight at week 5 = 137 pounds
Step 2: Calculate the change in weight.
The change in weight is calculated by subtracting the weight at week 5 from the initial weight:
Change in weight = Initial weight - Weight at week 5
Change in weight = 150 pounds - 137 pounds
Change in weight = 13 pounds
This indicates a loss of 13 pounds over the first five weeks.
Step 3: Calculate the change in time.
Since we are considering the first five weeks:
Change in time = Week 5 - Week 0
Change in time = 5 weeks - 0 weeks
Change in time = 5 weeks
Step 4: Formulate the ratio.
The ratio of the change in weight to the change in time is:
[tex]\[
\text{Ratio} = \frac{\text{Change in weight}}{\text{Change in time}} = \frac{13 \text{ pounds}}{5 \text{ weeks}}
\][/tex]
Step 5: Interpret the result.
The ratio [tex]\(\frac{-13}{5}\)[/tex] indicates that 13 pounds were lost over 5 weeks. This means that, on average, you lost [tex]\(2.6\)[/tex] pounds per week. Therefore, the correct interpretation is:
c. [tex]\(-\frac{13}{5}\)[/tex], 13 pounds was lost in 5 weeks.
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