Problem

The owners of a recreation area are filling a small pond with water. Let $W$ be the total amount of water in the pond (in liters). Let $T$ be the total number of minutes that water has been added. Suppose that $W=35 T+500$ gives $W$ as a function of $T$ during the next 70 minutes.

Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
\begin{tabular}{|l|l|l|}
\hline & Description of Values & Set of Values \\
\hline Domain: & \begin{tabular}{c}
number of minutes water has been added \\
amount of water in the pond (in liters)
\end{tabular} & (Choose one) \\
\hline Range: & \begin{tabular}{c}
Omumber of minutes water has been added \\
amount of water in the pond (in liters)
\end{tabular} & (Choose one) \\
\hline
\end{tabular}

Answer

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Answer

\(\boxed{\text{Range: amount of water in the pond (in liters), from 500 to 2950.}}\)

Steps

Step 1 :The domain of a function is the set of all possible input values (independent variable), which in this case is \(T\), the total number of minutes that water has been added. Since the problem states that the function is valid for the next 70 minutes, the domain is all real numbers from 0 to 70.

Step 2 :The range of a function is the set of all possible output values (dependent variable), which in this case is \(W\), the total amount of water in the pond. We can find the minimum and maximum values of \(W\) by substituting the minimum and maximum values of \(T\) into the function \(W=35T+500\).

Step 3 :Substitute \(T=0\) into the function to find the minimum value of \(W\): \(W=35*0+500=500\).

Step 4 :Substitute \(T=70\) into the function to find the maximum value of \(W\): \(W=35*70+500=2950\).

Step 5 :\(\boxed{\text{Domain: number of minutes water has been added, from 0 to 70.}}\)

Step 6 :\(\boxed{\text{Range: amount of water in the pond (in liters), from 500 to 2950.}}\)

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