To determine which table represents a car that increases, then decreases its speed over time, let's analyze the speed values given in each table.
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 Table 1, the speeds are: [45, 43, 41, 42, 43]
- From minute 5 to 7: Speed decreases from 45 to 41.
- From minute 7 to 9: Speed increases from 41 to 43.
This table shows a decrease followed by an increase, but we are looking for an increase followed by a decrease. Hence, Table 1 does not meet the criteria.
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 Table 2, the speeds are: [45, 47, 49, 48, 47]
- From minute 5 to 7: Speed increases from 45 to 49.
- From minute 7 to 9: Speed decreases from 49 to 47.
This table shows an increase followed by a decrease, which is what we are looking for. Thus, Table 2 meets the criteria.
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 Table 3, the speeds are: [45, 45, 45, 43, 41]
- From minute 5 to 7: Speed stays constant at 45.
- From minute 7 to 9: Speed decreases from 45 to 41.
This table shows no increase, only a decrease, so Table 3 does not meet the criteria.
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 Table 4, the speeds are: [45, 43, 41, 41, 41]
- From minute 5 to 7: Speed decreases from 45 to 41.
- From minute 7 to 9: Speed stays constant at 41.
This table shows a decrease followed by a constant speed, so Table 4 does not meet the criteria.
Conclusion: The table that shows the car's speed increasing and then decreasing is Table 2. It displays the required pattern of increasing speed followed by decreasing speed.
