To determine which table represents the speed of a car that first increases and then decreases, we need to focus on how the speed changes with time.
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]
In Table 1, the speeds are: 45, 43, 41, 42, 43 mph.
- From 5 to 7 minutes, the speed decreases (45 → 43 → 41).
- From 7 to 9 minutes, the speed fluctuates (41 → 42 → 43).
This table does not show a clear increase followed by a decrease. Hence, Table 1 is not the correct choice.
### 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]
In Table 2, the speeds are: 45, 47, 49, 48, 47 mph.
- From 5 to 7 minutes, the speed increases (45 → 47 → 49).
- From 7 to 9 minutes, the speed decreases (49 → 48 → 47).
This table clearly shows an increase in speed followed by a decrease. Therefore, Table 2 fits the condition of the speed increasing and then decreasing. Thus, Table 2 is the correct choice.
### 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]
In Table 3, the speeds are: 45, 45, 45, 43, 41 mph.
- From 5 to 9 minutes, the speed decreases steadily or remains constant.
This table shows a consistent decrease in speed without any increasing phase. Hence, Table 3 is also not the correct choice.
### 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]
In Table 4, the speeds are: 45, 43, 41, 41, 41 mph.
- From 5 to 9 minutes, the speed decreases initially and then stays constant.
This table does not indicate any increase in speed. Hence, Table 4 is not the correct choice.
Based on our analysis, the table that represents the speed of a car that increases and then decreases 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]
So, the correct table is Table 2.
