Answer :
Certainly! Let's analyze the given tables step by step to determine which one represents the car's speed increasing and then decreasing.
The car's speed should follow a pattern where it initially increases and then decreases.
### 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]
- From 5 to 6 minutes: Speed decreases (45 to 43)
- From 6 to 7 minutes: Speed decreases (43 to 41)
- From 7 to 8 minutes: Speed increases (41 to 42)
- From 8 to 9 minutes: Speed increases (42 to 43)
This pattern does not strictly follow an increase then 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]
- From 5 to 6 minutes: Speed increases (45 to 47)
- From 6 to 7 minutes: Speed increases (47 to 49)
- From 7 to 8 minutes: Speed decreases (49 to 48)
- From 8 to 9 minutes: Speed decreases (48 to 47)
This pattern follows an initial increase and then a decrease.
### 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]
- From 5 to 6 minutes: Speed stays the same (45 to 45)
- From 6 to 7 minutes: Speed stays the same (45 to 45)
- From 7 to 8 minutes: Speed decreases (45 to 43)
- From 8 to 9 minutes: Speed decreases (43 to 41)
This pattern does not strictly follow an increase then decrease.
### 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]
- From 5 to 6 minutes: Speed decreases (45 to 43)
- From 6 to 7 minutes: Speed decreases (43 to 41)
- From 7 to 8 minutes: Speed stays the same (41 to 41)
- From 8 to 9 minutes: Speed stays the same (41 to 41)
This pattern does not strictly follow an increase then decrease.
### Conclusion:
By analyzing each table:
- Table 1: No
- Table 2: Yes
- Table 3: No
- Table 4: No
The table that correctly represents the car's speed increasing and then decreasing is Table 2.
Therefore, the correct table is:
[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]
Thus, the answer is Table 2.
The car's speed should follow a pattern where it initially increases and then decreases.
### 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]
- From 5 to 6 minutes: Speed decreases (45 to 43)
- From 6 to 7 minutes: Speed decreases (43 to 41)
- From 7 to 8 minutes: Speed increases (41 to 42)
- From 8 to 9 minutes: Speed increases (42 to 43)
This pattern does not strictly follow an increase then 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]
- From 5 to 6 minutes: Speed increases (45 to 47)
- From 6 to 7 minutes: Speed increases (47 to 49)
- From 7 to 8 minutes: Speed decreases (49 to 48)
- From 8 to 9 minutes: Speed decreases (48 to 47)
This pattern follows an initial increase and then a decrease.
### 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]
- From 5 to 6 minutes: Speed stays the same (45 to 45)
- From 6 to 7 minutes: Speed stays the same (45 to 45)
- From 7 to 8 minutes: Speed decreases (45 to 43)
- From 8 to 9 minutes: Speed decreases (43 to 41)
This pattern does not strictly follow an increase then decrease.
### 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]
- From 5 to 6 minutes: Speed decreases (45 to 43)
- From 6 to 7 minutes: Speed decreases (43 to 41)
- From 7 to 8 minutes: Speed stays the same (41 to 41)
- From 8 to 9 minutes: Speed stays the same (41 to 41)
This pattern does not strictly follow an increase then decrease.
### Conclusion:
By analyzing each table:
- Table 1: No
- Table 2: Yes
- Table 3: No
- Table 4: No
The table that correctly represents the car's speed increasing and then decreasing is Table 2.
Therefore, the correct table is:
[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]
Thus, the answer is Table 2.
