Answer :
To determine which table represents a car that increases and then decreases its speed, let's examine each table one by one based on the given conditions.
### 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 min to 7 min: Speed decreases from 45 mph to 41 mph.
- From 7 min to 9 min: Speed increases from 41 mph to 43 mph.
This does not fit the pattern of first increasing and then decreasing. So, Table 1 is not valid.
### 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 min to 7 min: Speed increases from 45 mph to 49 mph.
- From 7 min to 9 min: Speed decreases from 49 mph to 47 mph.
This fits the pattern of first increasing and then decreasing. So, Table 2 is valid.
### 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 min to 7 min: Speed remains constant at 45 mph.
- From 7 min to 9 min: Speed decreases from 45 mph to 41 mph.
The speed does not increase initially. So, Table 3 is not valid.
### 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 min to 6 min: Speed decreases from 45 mph to 43 mph.
- From 6 min to 9 min: Speed decreases further from 43 mph to 41 mph.
The speed consistently decreases. So, Table 4 is not valid.
### Conclusion:
The table that could represent the car's speed increasing and then decreasing is Table 2.
### 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 min to 7 min: Speed decreases from 45 mph to 41 mph.
- From 7 min to 9 min: Speed increases from 41 mph to 43 mph.
This does not fit the pattern of first increasing and then decreasing. So, Table 1 is not valid.
### 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 min to 7 min: Speed increases from 45 mph to 49 mph.
- From 7 min to 9 min: Speed decreases from 49 mph to 47 mph.
This fits the pattern of first increasing and then decreasing. So, Table 2 is valid.
### 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 min to 7 min: Speed remains constant at 45 mph.
- From 7 min to 9 min: Speed decreases from 45 mph to 41 mph.
The speed does not increase initially. So, Table 3 is not valid.
### 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 min to 6 min: Speed decreases from 45 mph to 43 mph.
- From 6 min to 9 min: Speed decreases further from 43 mph to 41 mph.
The speed consistently decreases. So, Table 4 is not valid.
### Conclusion:
The table that could represent the car's speed increasing and then decreasing is Table 2.
