33. Error Analysis The table below shows the number of students enrolled in a high school personal finance course. A student says that a cubic model would best fit the data based on the ( n + 1 ) open n plus 1 close  Point Principle. Explain why a quadratic model might be more appropriate.

    Year	Number of Students Enrolled
    2000	50
    2004	65
    2008	94
    2010	110

34. Compare and Contrast The table shows the United States gross domestic product for selected years. Construct curves using cubic regression and quartic regression to model the data. Which curve seems most likely to model gross domestic product over the years?

    Year	1960	1970	1980	1990	2000
    GDP (billions $)	526.4	1038.5	2789.5	5803.1	9817.0

35. The table below shows the percentage of the U.S. labor force in unions for selected years between 1955 and 2005.

    Year	1955	1960	1965	1970	1975	1980	1985	1990	1995	2000	2005
    %	33.2	31.4	28.4	27.3	25.5	21.9	18.0	16.1	14.9	13.5	12.5

    1. Make a scatter plot of the data. Which kind of polynomial model seems to be most appropriate?
    2. Use a graphing calculator to find the type of model from part (a).
    3. Use the model you found in part (b) to predict the percent of the labor force in unions in the year 2020.
    4. Reasoning Do you have much confidence in this prediction? Explain.

C Challenge

36. Your friend's teacher showed the class a graph of a cubic polynomial in the ZDecimal window, which is [ − 4 . 7 , 4 . 7 ] left bracket negative 4 . 7 comma 4 . 7 right bracket  by [ − 3 . 1 , 3 . 1 ] . left bracket negative 3 . 1 comma 3 . 1 right bracket .  She then challenged the class to find the polynomial without using cubic regression on their calculators, and your friend succeeded. Follow your friend's steps and see if you can find the polynomial.

    

    1. The graph resembles a parabola with vertex (2, 0) near x = 2 . x equals 2 .  Find the equation in standard form for that parabola.
    2. Find the equation of a line in slope-intercept form through ( − 2 , 0 ) open negative 2 comma 0 close  with slope 1. Multiply the linear expression by the quadratic expression from part (a) to get a cubic. (Leave it in factored form.) Graph the cubic function. What do you notice about the zeros and the y-intercept of the cubic function?
    3. Multiply the cubic by a constant to change the y-intercept to 2. Graph the function to see if you've found the right polynomial. What is the function?

37. The graph below is that of a certain quartic polynomial in the ZDecimal window, which is [ − 4 . 7 , 4 . 7 ] left bracket negative 4 . 7 comma 4 . 7 right bracket  by [ − 3 . 1 , 3 . 1 ] . left bracket negative 3 . 1 comma 3 . 1 right bracket .  Find the equation of the quartic without using quartic regression on your calculator. You may leave it in factored form.

    

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