Chapter Two – Practice Exercises
2a)
While the owner in exercise 1a) was happy with the results of using elimination/substitution, she was curious to see if the results would differ using Newton’s Divided Difference (NDD) interpolation. You have decided to assist her by generating a cubic polynomial using NDD. (Solution given) The data is:
ABC Children's Party Company
| Maximum children attending the party | Cost per Child | Total Cost of Party |
|---|---|---|
| 10 | $37 | $370 |
| 25 | $28 | $700 |
| 50 | $22 | $1100 |
| 100 | $15 | $1500 |
Long Description
2b)
Using the same seven data points from the previous chapter select three data points and plug into the grid below to produce a quadratic solution. Simplify the resulting polynomial and put in standard form. Note solution given for the three bracketed points.
(Solution given)
Seven Data Points
| x | y or f(x) |
|---|---|
| -6.2 | -8 |
| [-3] | [-7] |
| -1.5 | -2.2 |
| [1] | [0.7] |
| 3.5 | 3 |
| 4.25 | 5 |
| [7.9] | [11] |
Long Description
Exercise 2b Answer Grid
Long Description
2c)
Add an additional data point and develop a 3rd degree (cubic) polynomial. Compare this to the solution from 2a) and decide whether or not it improves the interpolation. Note student answers may vary
The table provides pricing for different ranges of numbers of children attending a party. This increased flexibility the solution brings to this exercise will provide specific pricing by exact number attending, rather than a range.
These sample data points are to be used in the accompanying practice problem. Three of the seven are bracketed as they are used to provide a solution to this exercise.
Students should use the grid to record their solution. It includes columns for the independent variable, x the dependent variable f(x), the first divided difference and the second divided difference.
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