To find out which table could represent a car that increases, then decreases its speed, we need to analyze each set of speed data provided in the tables.
1. First Table:
[tex]\[
\begin{aligned}
\text{Time (min)} & : 5, \, 6, \, 7, \, 8, \, 9 \\
\text{Speed (mph)} & : 45, \, 43, \, 41, \, 42, \, 43 \\
\end{aligned}
\][/tex]
- From 45 to 43 (decrease)
- From 43 to 41 (decrease)
- From 41 to 42 (increase)
- From 42 to 43 (increase)
The speed first decreases, then increases, not showing the required pattern of increasing followed by decreasing.
2. Second Table:
[tex]\[
\begin{aligned}
\text{Time (min)} & : 5, \, 6, \, 7, \, 8, \, 9 \\
\text{Speed (mph)} & : 45, \, 47, \, 49, \, 48, \, 47 \\
\end{aligned}
\][/tex]
- From 45 to 47 (increase)
- From 47 to 49 (increase)
- From 49 to 48 (decrease)
- From 48 to 47 (decrease)
The speed pattern matches the requirement: it first increases and then decreases.
3. Third Table:
[tex]\[
\begin{aligned}
\text{Time (min)} & : 5, \, 6, \, 7, \, 8, \, 9 \\
\text{Speed (mph)} & : 45, \, 45, \, 45, \, 43, \, 41 \\
\end{aligned}
\][/tex]
- From 45 to 45 (constant)
- From 45 to 45 (constant)
- From 45 to 43 (decrease)
- From 43 to 41 (decrease)
The speed is constant for a period, then decreases. It doesn't show the required pattern of increasing followed by decreasing.
4. Fourth Table:
[tex]\[
\begin{aligned}
\text{Time (min)} & : 5, \, 6, \, 7, \, 8, \, 9 \\
\text{Speed (mph)} & : 45, \, 43, \, 41, \, 41, \, 41 \\
\end{aligned}
\][/tex]
- From 45 to 43 (decrease)
- From 43 to 41 (decrease)
- From 41 to 41 (constant)
- From 41 to 41 (constant)
The speed decreases and then remains constant. It does not show the required pattern of increasing followed by decreasing.
Based on this analysis, the Second Table:
[tex]\[
\begin{aligned}
\text{Time (min)} & : 5, \, 6, \, 7, \, 8, \, 9 \\
\text{Speed (mph)} & : 45, \, 47, \, 49, \, 48, \, 47 \\
\end{aligned}
\][/tex]
represents the speed of a car that increases and then decreases.
