Given:
The cost for the children’s party at the rollerskating rink is a function of n, the number of people in the party. The cost function, C is given by
[tex]C(n)=\left\{\begin{array}{ll}150, & 0<n \leq 12 \\260, & 12<n \leq 20 \\400, & 20<n \leq 30\end{array}\right.[/tex]
We need to determine the cost to have a party with 9 people and the cost to have a party with 20 people.
Cost of having the party:
From the given function, the cost of having the party for 9 people lies in the interval [tex]0<n \leq 12[/tex]
Hence, the cost of having the party for 9 people is 150.
Also, from the function, the cost of having the party for 20 people lies in the interval [tex]12<n \leq 20[/tex]
Hence, the cost of having the party for 20 people is 260.
it will cost #150 to have a party with 9 people, and it will cost #260 to have a party with 20 people
A piecewise function is used to relate multiple functions at different intervals
This means that:
[tex]n = 9[/tex]
When n = 9, the cost function is:
[tex]C(9) = 150[/tex]
Hence, it will cost #150 to have a party with 9 people
This means that:
[tex]n = 20[/tex]
When n = 20, the cost function is:
[tex]C(20) = 260[/tex]
Hence, it will cost #260 to have a party with 20 people
Read more about piecewise functions at:
https://brainly.com/question/3628123
