Now that you can determine whether or not a quadratic model is appropriate and you know several methods of formulating a quadratic function to fit the data, you are ready to formulate your own quadratic models for given contextual situations. For each situation below, formulate a quadratic model that fits the data.

  1. The table below shows the number of people, in millions, infected with the HIV virus each year from 1980 to 1996. Create a scatterplot of this data and find a quadratic model to fit the data. You can check your scatterplot and quadratic model below.
    2. Year HIV Infection
    (in millions)
    1980
    1981
    1982
    1983
    1984
    1985
    1986
    1987
    1988
    1989
    1990
    1991
    1992
    1993
    1994
    1995
    1996    		 0.2
    0.6
    1.1
    1.8
    2.7
    3.9
    5.3
    6.9
    8.7
    10.7
    13.0
    15.5
    18.5
    21.9
    25.9
    30.6
    36.2

  2. The table below shows the average hourly earnings from 1990 to 2002. Create a scatterplot of this data and find a quadratic model to fit the data. You can check your scatterplot and quadratic model below.
    3. Year Average Hourly Earnings
    (in dollars)
    1990
    1991
    1992
    1993
    1994
    1995
    1996
    1997
    1998
    1999
    2000
    2001
    2002    		 10.19
    10.50
    10.76
    11.03
    11.32
    11.64
    12.03
    12.49
    13.00
    13.47
    14.00
    14.53
    14.95