To identify the correct description of the values in both the domain and range of the function given by \( W = 15T + 600 \), we should first understand what \( T \) and \( W \) represent.
Given:
- \( T \) is the total number of minutes that water has been added.
- \( W \) is the total amount of water in the pond (in liters).
### Domain:
The domain of a function refers to the set of all possible input values (in this case, values of \( T \)) for which the function is defined.
Since \( T \) represents the number of minutes water has been added, and water is being added for the next 90 minutes:
- The minimum value of \( T \) is 0 minutes (when filling starts).
- The maximum value of \( T \) is 90 minutes (when filling ends).
Hence, the description of the domain is "the number of minutes water has been added," and the set of values for the domain is \( (0, 90) \).
### Range:
The range of a function refers to the set of all possible output values (in this case, values of \( W \)) resulting from the input values in the domain.
To find the range, we need to determine the minimum and maximum values of \( W \) when \( T \) ranges from 0 to 90 minutes.
Substitute the minimum and maximum values of \( T \) into the function \( W = 15T + 600 \):
- When \( T = 0 \): \( W = 15(0) + 600 = 600 \) liters.
- When \( T = 90 \): \( W = 15(90) + 600 = 1350 + 600 = 1950 \) liters.
Hence, the description of the range is "the amount of water in the pond (in liters)," and the set of values for the range is \( (600, 1950) \).
### Tabular Representation:
We can now fill in the table with the correct descriptions and sets of values:
\begin{tabular}{|l|l|l|}
\hline & Description of Values & Set of Values \\
\hline Domain: & \begin{tabular}{l}
\textbf{number of minutes water has been added} \\
amount of water in the pond (in liters)
\end{tabular} & \textbf{(0, 90)} \\
\hline Range: & \begin{tabular}{l}
number of minutes water has been added \\
\textbf{amount of water in the pond (in liters)}
\end{tabular} & \textbf{(600, 1950)} \\
\hline
\end{tabular}
