Question

1. the cost of holding a childrens birthday party at a roller - skating rink is a function of n, the number of people in the party. the cost function, c, can be represented with this set of rules:

\\(c(n)=\

$$\begin{cases}150, & 0 < n \\leq 12 \\\\260, & 12 < n \\leq 20 \\\\400, & 20 < n \\leq 30\\end{cases}$$

\\)
a. how much does it cost to have a party with 9 people?

Explanation:

Step1: Determine the interval for n = 9

We check which piece of the piece - wise function \(C(n)\) applies when \(n = 9\). The intervals are \(0\lt n\leq12\), \(12\lt n\leq20\), and \(20\lt n\leq30\). Since \(0\lt9\leq12\), we use the first piece of the function.

Step2: Find the cost for n = 9

For \(0\lt n\leq12\), the cost function is \(C(n)=150\). So when \(n = 9\), we substitute \(n = 9\) into this piece of the function. Since \(9\) is in the interval \(0\lt n\leq12\), \(C(9)=150\).

Answer:

The cost to have a party with 9 people is 150.