A museum charges $4 per person for a guided tour with a group of 1 to 12 people or a fixed $52 fee for a group of 13 or more people. Write a function relating the number of people, n, to the cost, C.


To express the cost $ C $ as a function of the number of people $ n $, we need to consider two cases based on the number of people in the group:

1. **If the group has between 1 and 12 people**, the cost is calculated at $4 per person, so the cost will be $ C = 4n $.

2. **If the group has 13 or more people**, the cost is fixed at $52, regardless of the number of people, so $ C = 52 $.

Thus, the function $ C(n) $, which relates the number of people $ n $ to the cost $ C $, can be written as:

\[
C(n) = 
\begin{cases} 
4n & \text{if } 1 \leq n \leq 12 \\
52 & \text{if } n \geq 13 
\end{cases}
\]

This is a piecewise function that defines the cost based on the group size.

Would you like further clarification on how piecewise functions work, or details on any part of this problem?

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**Related questions:**

1. How do piecewise functions work in different mathematical contexts?
2. Can we use this function to compute the cost for fractional values of $ n $?
3. How would the function change if the price per person were different for larger groups?
4. What happens to the function if we introduce discounts for larger groups?
5. How would you graph this piecewise function?

**Tip:** Piecewise functions are helpful when different conditions apply in different situations, such as pricing models or tax rates.

A museum charges $4 per person for a guided tour with a group of 1 to 12 people or a fixed $52 fee for a group of 13 or more people. Write a function relating the number of people, n, to the cost, C.

Learn how to model the cost of a museum guided tour using a piecewise function. The cost is $4 per person for groups of 1 to 12 people and a fixed $52 for groups of 13 or more. This problem introduces piecewise functions and linear relationships, ideal for students in Grades 8-10.

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