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*+25*T*500

gives

*W*

as a function of

*T*

during the next

90

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.

**Description of ValuesSet of ValuesDomain:**

amount of water in the pond (in liters)

number of minutes water has been added

Domain: Set of Values▼(Choose one)

**Range:**

amount of water in the pond (in liters)

number of minutes water has been added

Range: Set of Values▼(Choose one)

Let's break this down:

### The given equation:
\[ W = 25T + 500 \]

Here:
- **W** represents the total amount of water in the pond (in liters).
- **T** represents the number of minutes that water has been added.

### **Domain:**
The **domain** refers to the set of possible values for **T**, the independent variable, which represents the number of minutes water has been added. The problem specifies that the water is being added for the next **90 minutes**. Therefore, the domain is:
- **Description:** The number of minutes water has been added.
- **Set of Values:** [0, 90] (i.e., T can range from 0 to 90 minutes).

### **Range:**
The **range** refers to the set of possible values for **W**, the dependent variable, which represents the amount of water in the pond. Using the equation \( W = 25T + 500 \), we can determine the range by finding the minimum and maximum values of **W** over the domain:
- When \( T = 0 \), \( W = 25(0) + 500 = 500 \).
- When \( T = 90 \), \( W = 25(90) + 500 = 2250 + 500 = 2750 \).

Thus, the range is:
- **Description:** The amount of water in the pond (in liters).
- **Set of Values:** [500, 2750] (i.e., the amount of water ranges from 500 to 2750 liters).

### Final Answer:
- **Domain:**
  - **Description:** The number of minutes water has been added.
  - **Set of Values:** [0, 90]
  
- **Range:**
  - **Description:** The amount of water in the pond (in liters).
  - **Set of Values:** [500, 2750]

---

Would you like further details on how we derived these values? Here are 5 related questions to expand on this topic:

1. How would the equation change if water was being removed from the pond instead of added?
2. What happens to the domain and range if the time is extended beyond 90 minutes?
3. How does the slope (25 liters per minute) affect the filling rate of the pond?
4. What does the initial value of 500 liters represent in this context?
5. Can we represent this function graphically, and what would the graph look like?

**Tip:** When interpreting a function, always identify what each variable represents and the real-world constraints on the domain and range!

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 = 25T + 500 gives W as a function of T during the next 90 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.

Learn how to determine the domain and range for a linear function describing water being added to a pond, W = 25T + 500. This problem involves concepts of linear functions, domain, and range. Suitable for students in Grades 8-10.

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