1. Lesson 3

1.8. Explore 4

Mathematics 30-2 Module 4

Module 4: Polynomials

 

Consider the following data. The table shows the cost of one dozen eggs from 1913 to present day.

 

Year Since 1913 0 10 15 22 30 35 44 50 60 72 79 84 88 99
Cost of One Dozen Eggs ($) 0.35 0.48 0.60 0.75 0.64 0.60 0.72 0.88 0.90 1.00 1.22 1.54 1.70 2.10
 

This is a photo of 10 eggs.

iStockphoto/Thinkstock

 

 


 

Draw a scatter plot of the data. Then compare your scatter plot with the following.

 

 
This is a scatter plot showing the egg data.

 

What do you notice? Is the data linear? quadratic? neither?

 

The data is neither linear nor quadratic and would best be modelled by a cubic function.

 

Use your graphing calculator to find the cubic regression equation (much like you have found the linear regression equations and quadratic regression equations).

 

The equation from your calculator (after some rounding) should be

 

 

y = 0.000 004 3x3 − 0.000 45x2 + 0.02x + 0.36

 

Plotting the cubic curve of best fit yields the following graph:

This is a cubic scatter plot showing the egg data with a curve of best fit superimposed.

 

Self-Check 2
  1. Using the model from the egg example, y = 0.000 004 3x3 − 0.000 45x2 + 0.02x + 0.36, what was the cost of eggs in 1955? Answer
  2. In what year was the cost of eggs $1.30 per dozen? Answer