Chapter One – Practice Exercises

1a)

The owner of the ABC Children’s Party Company has offered a limited menu of pricing options depending on the number of children attending the party. The available prices are included in the table below:

ABC Children's Party Company

Long Description

The prices cover the cost plus acceptable profit and have worked well in the past. To improve the companies competitiveness, the owner would like to offer more flexible pricing that is specific to the actual number of children. She would like to develop a cubic (3rd degree) polynomial that will generate the unit price when she inputs the expected number of children attending the party. To develop this polynomial the student must use the algebraic technique of substitution (elimination) discussed in this chapter.
(Solution Given)
 

1b)

This exercise offers practice in using basic matrix commands either manually or in a spreadsheet program to solve n-equations in n-unknowns.
(Solution given for 2nd to 5th row of data)

Given the following data points, develop a polynomial that will interpolate any value of p(x) on the given interval, for the bracketed points. It will result in a third-degree polynomial:

Exercise 1b Sample Data Point

Long Description

Tables  are provided to assist students

Long Description

1c)

Select any three data points from the above table and develop a 2nd degree (quadratic) Polynomial.