a museum charges $15 per person for a guided tour with a group of 1 to 9 people of a fixed $65 for a group of 10 or more people. write a function relating the number of people, p, to the cost, c

We can define a piecewise function to relate the number of people $ p $ to the cost $ c $, based on the two different pricing schemes:

- For groups with $ 1 \leq p \leq 9 $, the cost is $15 per person.
- For groups with $ p \geq 10 $, the cost is a fixed $65.

The function $ c(p) $ can be written as:

\[
c(p) =
\begin{cases} 
15p, & 1 \leq p \leq 9 \\
65, & p \geq 10
\end{cases}
\]

This function describes how the cost $ c $ depends on the number of people $ p $ in the group.

Would you like further details on how to graph this, or do you have any other questions?

Here are 5 related questions:
1. How would the function change if the fixed cost for groups of 10 or more was $80 instead?
2. How does this function behave when $ p = 9 $ and $ p = 10 $?
3. What would happen if there was a minimum group size of 3 people?
4. Can you express this function using an absolute value or a different form?
5. How would you find the break-even point between these two pricing schemes?

**Tip**: Piecewise functions are useful for modeling situations where different rules apply to different intervals of input.

A museum charges $15 per person for a guided tour with a group of 1 to 9 people or a fixed $65 for a group of 10 or more people. Write a function relating the number of people, p, to the cost, c.

Learn how to create a piecewise function to determine the cost of a museum tour based on group size. This problem involves algebraic concepts and piecewise functions, with a step-by-step solution for understanding different pricing schemes. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation