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Sagot :
To determine which table accurately represents a car that first increases its speed and then decreases it, we need to analyze the data in each table and check if there is an initial increase followed by a decrease.
Let's examine each table one by one.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 43 \rightarrow 41 \)[/tex] (decreasing)
- From 7 to 9 minutes: [tex]\( 41 \rightarrow 42 \rightarrow 43 \)[/tex] (increasing)
This table shows the speed first decreasing and then increasing, which does not match the required pattern.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 47 \rightarrow 49 \)[/tex] (increasing)
- From 7 to 9 minutes: [tex]\( 49 \rightarrow 48 \rightarrow 47 \)[/tex] (decreasing)
This table shows the speed first increasing and then decreasing, which matches the required pattern.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 45 \rightarrow 45 \)[/tex] (constant)
- From 7 to 9 minutes: [tex]\( 45 \rightarrow 43 \rightarrow 41 \)[/tex] (decreasing)
This table shows the speed first being constant and then decreasing, which does not match the required pattern.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 43 \rightarrow 41 \)[/tex] (decreasing)
- From 7 to 9 minutes: [tex]\( 41 \rightarrow 41 \rightarrow 41 \)[/tex] (constant)
This table shows the speed first decreasing and then being constant, which does not match the required pattern.
### Conclusion
The table that shows the speed of the car 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 table is the second table.
Let's examine each table one by one.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 43 \rightarrow 41 \)[/tex] (decreasing)
- From 7 to 9 minutes: [tex]\( 41 \rightarrow 42 \rightarrow 43 \)[/tex] (increasing)
This table shows the speed first decreasing and then increasing, which does not match the required pattern.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 47 \rightarrow 49 \)[/tex] (increasing)
- From 7 to 9 minutes: [tex]\( 49 \rightarrow 48 \rightarrow 47 \)[/tex] (decreasing)
This table shows the speed first increasing and then decreasing, which matches the required pattern.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 45 \rightarrow 45 \)[/tex] (constant)
- From 7 to 9 minutes: [tex]\( 45 \rightarrow 43 \rightarrow 41 \)[/tex] (decreasing)
This table shows the speed first being constant and then decreasing, which does not match the required pattern.
### 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]
- From 5 to 7 minutes: [tex]\( 45 \rightarrow 43 \rightarrow 41 \)[/tex] (decreasing)
- From 7 to 9 minutes: [tex]\( 41 \rightarrow 41 \rightarrow 41 \)[/tex] (constant)
This table shows the speed first decreasing and then being constant, which does not match the required pattern.
### Conclusion
The table that shows the speed of the car 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 table is the second table.
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