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You began membership in a new health and fitness club, which provides access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, [tex] w [/tex], as a function of time, [tex] t [/tex], over an eight-week period.

[tex]
\[
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
\text{Time (weeks)} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\text{Weight (lb)} & 150 & 144 & 143 & 141 & 140 & 137 & 137 & 132 & 129 \\
\hline
\end{tabular}
\]
[/tex]

Write the ratio of the change in weight for the first five weeks to the change in time for the first five weeks. Interpret the meaning of this ratio.

A. [tex]\frac{-13}{5}[/tex], 5 pounds was lost in 13 weeks

B. [tex]\frac{5}{13}[/tex], 13 pounds was gained in 5 weeks

C. [tex]\frac{-13}{5}[/tex], 13 pounds was lost in 5 weeks

D. [tex]\frac{5}{-13}[/tex], 5 pounds was lost in 13 weeks

Answer :

To solve this problem, we need to calculate the ratio of the change in weight over the first five weeks to the change in time. Let's go through the steps:

1. Identify the start and end weights for the first five weeks:
- Initial weight at the start (week 0): 150 pounds
- Weight after five weeks (week 5): 137 pounds

2. Calculate the total change in weight:
- Change in weight = Weight after five weeks - Initial weight
- Change in weight = 137 - 150 = -13 pounds

3. Determine the change in time:
- From week 0 to week 5, the change in time is 5 weeks.

4. Calculate the ratio of the change in weight to the change in time:
- Ratio = Change in weight / Change in time
- Ratio = -13 / 5

5. Interpret the meaning of the ratio:
- The negative sign indicates that weight was lost.
- The ratio of [tex]\(-\frac{13}{5}\)[/tex] tells us that 13 pounds were lost in 5 weeks.

Thus, the correct interpretation is:

c. [tex]\(-\frac{13}{5}\)[/tex], 13 pounds was lost in 5 weeks.

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Rewritten by : Barada