Answer :
To determine which table represents the car's speed as it increases and then decreases, let us analyze each table provided.
### Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 43 & 41 & 42 & 43 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Decreases from 45 to 41 (from minute 5 to 7).
- Increases from 41 to 43 (from minute 7 to 9).
This pattern is not consistent with a general increase followed by a decrease.
### Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 47 & 49 & 48 & 47 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Increases from 45 to 49 (from minute 5 to 7).
- Decreases from 49 to 47 (from minute 7 to 9).
This pattern matches the requirement of an increase in speed followed by a decrease in speed.
### Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 45 & 45 & 43 & 41 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Remains constant from minute 5 to 7 (45 mph).
- Decreases from 45 to 41 (from minute 7 to 9).
This pattern does not match the required increasing and then decreasing behavior.
### Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 43 & 41 & 41 & 41 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Decreases continuously from 45 to 41 (from minute 5 to 7, and remains constant till minute 9).
This pattern does not match the required increasing and then decreasing behavior.
Through analyzing each table, we see that Table 2 demonstrates the car's speed increasing and then decreasing correctly. Thus, the suitable table is:
[tex]\[ \boxed{2} \][/tex]
### Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 43 & 41 & 42 & 43 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Decreases from 45 to 41 (from minute 5 to 7).
- Increases from 41 to 43 (from minute 7 to 9).
This pattern is not consistent with a general increase followed by a decrease.
### Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 47 & 49 & 48 & 47 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Increases from 45 to 49 (from minute 5 to 7).
- Decreases from 49 to 47 (from minute 7 to 9).
This pattern matches the requirement of an increase in speed followed by a decrease in speed.
### Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 45 & 45 & 43 & 41 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Remains constant from minute 5 to 7 (45 mph).
- Decreases from 45 to 41 (from minute 7 to 9).
This pattern does not match the required increasing and then decreasing behavior.
### Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 43 & 41 & 41 & 41 \\ \hline \end{array} \][/tex]
In this table, the speed:
- Decreases continuously from 45 to 41 (from minute 5 to 7, and remains constant till minute 9).
This pattern does not match the required increasing and then decreasing behavior.
Through analyzing each table, we see that Table 2 demonstrates the car's speed increasing and then decreasing correctly. Thus, the suitable table is:
[tex]\[ \boxed{2} \][/tex]
