Question

1. party selena is planning a birthday party for her little sister at a local zoo. the price depends on the number of children that attend the party. the price per child is normally $7. however, if there are more than 10 children in a group, the group can pay a $20 fee plus $4 per child. write a piece - wise function that best models the cost of the party c(x) if selena invites x children?

Explanation:

Step1: Define the cases

We have two - case based on the number of children \(x\).

Step2: Case 1: \(x\leq10\)

The cost per child is \(7\) dollars. The fixed fee is \(20\) dollars. So the cost function \(c(x)=20 + 7x\) for \(x\leq10\).

Step3: Case 2: \(x > 10\)

The cost per child is \(4\) dollars and the fixed fee is \(20\) dollars. So the cost function \(c(x)=20+4x\) for \(x > 10\).

Answer:

\[c(x)=

$$\begin{cases}20 + 7x, &x\leq10\\20+4x, &x > 10\end{cases}$$

\]