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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

MODELING WITH DATA Annual retail sales in the United States from 2000 through the year 2008 (in billions of dollars) are given in the following table:

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008
Sales 2.988 3.068 3.134 3.267 3.480 3.698 3.882 4.005 3.959
  1. a. Let t = 0 correspond to 2000, and use QuadReg to find a second-degree polynomial regression model based on the given data.
  2. b. Plot the graph of the function found in part (a) in the viewing window [0, 8] × [0, 5].
  3. c. What were the annual retail sales in the United States in 2006 (t = 6)?
  4. d. Approximately how fast were the retail sales changing in 2006 (t = 6)?

Source: U.S. Census Bureau.

(a)

To determine
The second degree polynomial regression model for the given data.

Explanation

Given:

The annual retail sales (billion dollars) in United States from the year 2000 to 2008 are shown in given table.

YearSales
20002.988
20013.068
20023.134
20033.267
20043.480
20053.698
20063.882
20074.005
20083.959

For the year 2000 the value of t is 0.

Calculation:

Since t=0 for the year 2000, therefore the above table is written as shown below.

tSales
02.988
13.068
23.134
33.267
43.480
53.698
63.882
74.005
83.959

Use graphing calculator to find the quadratic polynomial that best fits the data.

First press “ON” button on graphical calculator, press STAT key, select option 1: Edit and press ENTER key

(b)

To determine

To sketch: The graph of the function found in part (a) in the viewing window [0,8]×[0,5] .

(c)

To determine
The annual retail sales in the United States in the year 2006.

(d)

To determine
The rate of change of retail sales in 2006.

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