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The problem is asking for a linear cost function for the situation where a ski resort charges a snowboard rental fee of $10 plus $5.25 per hour.

### Let's break this down:

1. **Fixed Cost**: The ski resort charges a **fixed fee of $10**, regardless of the number of hours rented.
2. **Hourly Rate**: The resort charges an additional **$5.25 per hour**.

### Linear Cost Function:

We are asked to express the total cost $ C(t) $ as a function of the number of hours $ t $ the snowboard is rented.

- The **fixed fee** is always $10.
- The **variable part** (dependent on time) is $5.25 per hour, so for $ t $ hours, the cost will be $ 5.25t $.

Thus, the cost function is:
\[
C(t) = 10 + 5.25t
\]

### Identifying Variables:

The correct answer for what $ C(t) $ represents is **option A**, which states:
- **$ C(t) $** represents the cost of renting a snowboard for $ t $ hours.

Do you have any questions, or would you like more details on any part of the problem?

### Related Questions:
1. How would the cost function change if the resort increased the hourly rate to $6 per hour?
2. What is the total cost of renting the snowboard for 3 hours using the given cost function?
3. How would the equation change if the resort gave a discount after 5 hours of rental?
4. What would the slope represent in the context of this problem?
5. What would the cost function look like if there was no fixed cost but a higher hourly rate of $7 per hour?

### Tip:
When dealing with linear functions, always identify the fixed cost (y-intercept) and the rate of change (slope), which corresponds to the variable part of the problem.

A ski resort charges a snowboard rental fee of $10 plus $5.25 per hour. What is the linear cost function and what do the variables represent?

Learn how to create a linear cost function for a snowboard rental situation with a fixed fee of $10 and an hourly rate of $5.25. This problem covers linear functions and algebraic representation. Suitable for students in Grades 7-10.

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