To find the constant rate of change in the given table, we need to determine how the wage changes with respect to time. This is found by calculating the rate of change between any two points in the table.
The table provided is:
\begin{tabular}{|l|l|l|l|l|}
\hline
Time [tex]$(h)$[/tex] & 0 & 1 & 2 & 3 \\
\hline
Wage [tex]$(\$[/tex])[tex]$ & 0 & 9 & 18 & 27 \\
\hline
\end{tabular}
To find the rate of change, we use the formula:
\[
\text{Rate of change} = \frac{\Delta \text{Wage}}{\Delta \text{Time}}
\]
We can pick any two adjacent points from the table to calculate this. Let’s use the first two points:
For Time \( t = 0 \) and \( t = 1 \):
- Wage at \( t = 0 \) is \$[/tex]0
- Wage at [tex]\( t = 1 \)[/tex] is \[tex]$9
So, the change in wage (\(\Delta \text{Wage}\)) is:
\[
9 - 0 = 9 \text{ dollars}
\]
And the change in time (\(\Delta \text{Time}\)) is:
\[
1 - 0 = 1 \text{ hour}
\]
Therefore, the rate of change is:
\[
\frac{\Delta \text{Wage}}{\Delta \text{Time}} = \frac{9 \text{ dollars}}{1 \text{ hour}} = 9 \text{ dollars per hour}
\]
Thus, the constant rate of change for the table is:
\[
\$[/tex]9/\text{hour}
\]
The correct answer is:
A) \$9 / hour
