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Thread: Polynomial Functions

  1. #1
    Apr 2009

    Polynomial Functions

    The amounts y of the Federal budget deficit over a 15 year period in billions of dollars are as
    follows. (1977, 53.6), (1978, 59.2), (1979, 40.2), (1980, 73.8), (1981, 78.9), (1982, 127.9),
    (1983, 207.8), (1984, 185.3), (1985, 212.3), (1986, 221.2), (1987, 149.7), (1988, 155.1),
    (1989, 153.4), (1990, 220.4), (1991, 320.1)
    (a) Let t be the time in years, with t = 0 corresponding to 1984. Use the regression capabilities
    to find an appropriate model for the data. What is the domain of the model?
    Try linear model: y = ax + b, quadratic model: y = ax^2; + bx; + c,
    cubic model: y = ax^3; + bx^2; + cx; + d, or a quadric model: y = ax^4; + bx^3; + cx^2; + dx; + e.
    Modify the solved example.
    (b) Graph the data and model. Find the best fitting model among the above four models.
    Answer the following questions for the best fit model:
    (c) For which year does the model most accurately estimate the actual data? During which
    year is it least accurate?
    (d) By extending the curve on the hard copy, estimate the budget deficit for 1992.
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  2. #2
    MHF Contributor
    Mar 2007


    Where are you having trouble?

    a) You plugged the given values into your graphing calculator, punched the buttons like they taught you in class, and... then what?

    b) You graphed your four equations, looked at the picture showing the equations and the scatterplot, and... then what?

    c) You compared the dots in the scatterplot with the line for your chosen equation, and... then what?

    d) You plugged "8" in for "t" in your equation, and... then what?

    Please be complete. Thank you!
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  3. #3
    Jul 2009

    Polynomial Functions of Higher Degree

    I'm having trouble trying to figure out how to solve this problem. I have graphed the equation and I still don't understand how the Intermediate Value Theorem works. If anyone could help I would highly appreciate it. Thanks in advance.

    Instructions: (a) Use the Intermediate Value Theorem and a graphing utility to find intervals of length 1 in which the polynomial function is guaranteed to have a zero.
    (b) Use the root feature of a graphing utility to approximate the zeros of the function.

    Problem: h(x)= x^4-10x^2+2
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