To determine which table represents a car's speed first increasing and then decreasing, you need to examine the speed values in each table.
Here are the steps:
1. List the Speeds:
- Table 1:
[tex]\[
\begin{array}{|l|c|c|c|c|c|}
\hline
\text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\
\hline
\text{Speed (mph)} & 45 & 43 & 41 & 42 & 43 \\
\hline
\end{array}
\][/tex]
- Table 2:
[tex]\[
\begin{array}{|l|c|c|c|c|c|}
\hline
\text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\
\hline
\text{Speed (mph)} & 45 & 47 & 49 & 48 & 47 \\
\hline
\end{array}
\][/tex]
- Table 3:
[tex]\[
\begin{array}{|l|c|c|c|c|c|}
\hline
\text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\
\hline
\text{Speed (mph)} & 45 & 45 & 45 & 43 & 41 \\
\hline
\end{array}
\][/tex]
- Table 4:
[tex]\[
\begin{array}{|l|c|c|c|c|c|}
\hline
\text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\
\hline
\text{Speed (mph)} & 45 & 43 & 41 & 41 & 41 \\
\hline
\end{array}
\][/tex]
2. Check Each Table:
- Table 1: The speeds are [tex]\(45, 43, 41, 42, 43\)[/tex]. Here, the speed decreases first, then increases, then increases again. This one does not fit the required pattern of first increasing then decreasing.
- Table 2: The speeds are [tex]\(45, 47, 49, 48, 47\)[/tex]. Here, the speed increases from 45 to 49 and then decreases from 49 to 47. This one fits the pattern of first increasing then decreasing.
- Table 3: The speeds are [tex]\(45, 45, 45, 43, 41\)[/tex]. Here, the speed remains constant initially and then decreases. This one does not fit the required pattern of first increasing then decreasing.
- Table 4: The speeds are [tex]\(45, 43, 41, 41, 41\)[/tex]. Here, the speed decreases first and then stays constant. This one does not fit the required pattern of first increasing then decreasing.
3. Conclusion:
The table that represents the car's speed first increasing and then decreasing is:
[tex]\[
\begin{array}{|l|c|c|c|c|c|}
\hline
\text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\
\hline
\text{Speed (mph)} & 45 & 47 & 49 & 48 & 47 \\
\hline
\end{array}
\][/tex]
Therefore, the correct answer is the second table.
