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!