High School

You began membership in a new health and fitness club which has 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][tex]$t$[/tex][/tex], over an eight-week period.

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

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 :

The ratio of the change in weight for the first five weeks C. [tex]\frac{-13}{5}[/tex], 13 pounds was lost in 5 weeks.

Use the data provided in the table to calculate this ratio step-by-step.

The table provides the following weights at the corresponding weeks:

Time (weeks)012345Weight (lb)150144143141140137

First, find the change in weight over the first five weeks:

Initial weight at week 0: 150 lb

Weight at week 5: 137 lb

Change in weight: 150 - 137 = 13 lb

Next, find the change in time over the first five weeks:

Initial time: 0 weeks

Time at week 5: 5 weeks

Change in time: 5 - 0 = 5 weeks

The ratio of the change in weight to the change in time is:

Ratio: [tex]\frac{-13}{5}[/tex]

The negative sign indicates a decrease in weight.

This ratio means that over the first five weeks, the person lost 13 pounds. The negative sign signifies that the weight was reduced, and the ratio of [tex]\frac{-13}{5}[/tex] indicates that for each week, on average, approximately 2.6 pounds were lost.

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