   Chapter 2.3, Problem 19TE

Chapter
Section
Textbook Problem

Nicotine Content of Cigarettes Even as measures to discourage smoking have been growing more stringent in recent years, the nicotine content of cigarettes has been rising, making it more difficult for smokers to quit. The following table gives the average amount of nicotine in cigarette smoke (in milligrams) from 1999 through 2004: Year 1999 2000 2001 2002 2003 2004 Yield per Cigarette 1.71 1.81 1.85 1.84 1.83 1.89 a. Use QuartReg to find a fourth-degree polynomial regression model for the data. Let t = 0 correspond to the beginning of 1999. b. Plot the graph of the function f found in part (a), using the viewing window [0, 5] × [0, 2]. c. Compute the values of f(t) for t = 0, 1, 2, 3, 4, and 5. d. If the trend continued, what was the average amount of nicotine in cigarettes in 2005? Source: Massachusetts Tobacco Control Program.

(a)

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

Explanation

Given information:

The average amount of nicotine in cigarette smoke (in milligrams) is given in the table.

 Year Yield per Cigarette 1999 1.71 2000 1.81 2001 1.85 2002 1.84 2003 1.83 2004 1.89

For the initial year 1999 the value of t is 0.

Calculation:

The value of t is 0 for the initial year 1999, therefore the given table is written as shown below.

 Year Yield per Cigarette 0 1.71 1 1.81 2 1.85 3 1.84 4 1.83 5 1.89

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

First press “ON” button on graphical calculator, press STAT key, select option 1: Edit and press ENTER key. Then enter the given data in the columns of graphing calculator. The display shows the table as shown in Figure (1).

(b)

To determine

To sketch: The graph of the function found in part (a) in the viewing window [0,5]×[0,2] .

(c)

To determine
The values of f(t) for t=0,1,2,3,4 and 5.

(d)

To determine
The average amount of nicotine in cigarettes in 2005.

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