The table shows the national expenditures for health care in the United States for selected years, with projections to 2020.
Year __________________ National Expenditures for Health Care (billions)
1960 ....................................................... $28
1970 ........................................................ 75
1980 ....................................................... 254
1990 ....................................................... 714
1995 ..................................................... 1017
2000 ..................................................... 1353
2005 ..................................................... 1981
2010 .................................................... 2954
2015 .................................................... 3308
2020 .................................................... 4487
(a) Use a scatter plot with x as the number of years past 1950 and y as the total expenditures for health care (in billions) to identify what type (or types) of function(s) would make a good model for these data.
(b) Find a power model and a quadratic model for the data.
(c) Which model from part (b) more accurately approximates the data point for 2020?
(d) Use the quadratic model to predict the 2025 expenditures for national health care?