When Brady jogs laps around a circular path with a fountain at the center, his distance from the fountain changes in a specific manner due to the nature of circular motion. Let us examine each table and determine which one correctly describes his distance from the fountain over time:
1. In the first table:
\begin{tabular}{|c|c|}
\hline Time & Distance (feet) \\
\hline 0 & 50 \\
\hline 2 & 60 \\
\hline 4 & 70 \\
\hline 6 & 80 \\
\hline 8 & 100 \\
\hline
\end{tabular}
The distance always increases linearly. This is unrealistic for jogging in a circular path, as he should eventually return to his starting distance.
2. In the second table:
\begin{tabular}{|c|c|}
\hline Time & Distance (feet) \\
\hline 0 & 50 \\
\hline 2 & 60 \\
\hline 4 & 70 \\
\hline 6 & 60 \\
\hline 8 & 50 \\
\hline
\end{tabular}
The distance first increases to a maximum point and then decreases back to the starting point. This cyclical pattern is realistic for circular jogging paths, as he moves further from and closer to the fountain as he jogs around the path.
3. In the third table:
\begin{tabular}{|c|c|}
\hline Time & Distance (feet) \\
\hline 0 & 50 \\
\hline 2 & 50 \\
\hline 4 & 50 \\
\hline 6 & 50 \\
\hline 8 & 50 \\
\hline
\end{tabular}
The distance remains constant at 50 feet. This is not realistic for jogging in a circular path, as his distance should change as he jogs around the entire path.
4. In the fourth table:
\begin{tabular}{|c|c|}
\hline Time & Distance (feet) \\
\hline 0 & 50 \\
\hline 2 & 40 \\
\hline 4 & 30 \\
\hline 6 & 20 \\
\hline 8 & 10 \\
\hline
\end{tabular}
The distance always decreases linearly. This is unrealistic since it doesn't accommodate for the circular nature of his jogging path, which should bring him back to his starting distance.
From the analysis, the second table correctly represents Brady's distance from the fountain after jogging around the park for a given number of minutes. Therefore, the table that could represent Brady's distance from the fountain is:
[tex]\[ \boxed{2} \][/tex]
