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Representing a Relationship Numerically

Brady jogs laps around a circular park with a fountain at the center. Which table could represent Brady's distance from the fountain after jogging around the path for a number of minutes?

\begin{tabular}{|c|c|}
\hline
Time (minutes) & Distance (feet) \\
\hline
0 & 50 \\
\hline
2 & 60 \\
\hline
4 & 70 \\
\hline
6 & 80 \\
\hline
8 & 100 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
Time (minutes) & Distance (feet) \\
\hline
0 & 50 \\
\hline
2 & 60 \\
\hline
4 & 70 \\
\hline
6 & 60 \\
\hline
8 & 50 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
Time (minutes) & Distance (feet) \\
\hline
0 & 50 \\
\hline
2 & 50 \\
\hline
4 & 50 \\
\hline
6 & 50 \\
\hline
8 & 50 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
Time (minutes) & Distance (feet) \\
\hline
0 & 50 \\
\hline
2 & 40 \\
\hline
4 & 30 \\
\hline
6 & 20 \\
\hline
8 & 10 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
We need to determine which table correctly represents Brady's distance from the fountain after jogging for various times. Let's analyze each table one by one.

### Table Analysis:

#### 1. Table 1:
[tex]\[ \begin{tabular}{|c|c|} \hline Time (minutes) & Distance (feet) \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 80 \\ \hline 8 & 100 \\ \hline \end{tabular} \][/tex]
Observation: The distance from the fountain increases linearly over time. This suggests Brady is consistently moving away from the fountain.

#### 2. Table 2:
[tex]\[ \begin{tabular}{|c|c|} \hline Time (minutes) & Distance (feet) \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 60 \\ \hline 8 & 50 \\ \hline \end{tabular} \][/tex]
Observation: The distance first increases and then decreases, suggesting a pattern where Brady may be jogging back and forth, or possibly around a circular path and returning to the starting point.

#### 3. Table 3:
[tex]\[ \begin{tabular}{|c|c|} \hline Time (minutes) & Distance (feet) \\ \hline 0 & 50 \\ \hline 2 & 50 \\ \hline 4 & 50 \\ \hline 6 & 50 \\ \hline 8 & 50 \\ \hline \end{tabular} \][/tex]
Observation: The distance remains constant over time, implying Brady is stationary or moving in a way that keeps the distance from the fountain unchanged.

#### 4. Table 4:
[tex]\[ \begin{tabular}{|c|c|} \hline Time (minutes) & Distance (feet) \\ \hline 0 & 50 \\ \hline 2 & 40 \\ \hline 4 & 30 \\ \hline 6 & 20 \\ \hline 8 & 10 \\ \hline \end{tabular} \][/tex]
Observation: The distance decreases linearly over time, indicating Brady is moving towards the fountain.

Given that Brady is jogging laps around a circular park, we should expect a pattern that reflects a continuous movement rather than a movement away or towards a point.

### Conclusion:
The most plausible table is the one where Brady's distance from the fountain increases consistently as he jogs around the park, reflecting that he is moving in a specific direction consistently. This would correspond to Table 1:

[tex]\[ \begin{tabular}{|c|c|} \hline Time (minutes) & Distance (feet) \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 80 \\ \hline 8 & 100 \\ \hline \end{tabular} \][/tex]

Hence, Table 1 accurately represents Brady's distance from the fountain after jogging laps around the circular park.

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