Chapter 2.5, Problem 36E

National health care The table shows the national expenditures for health care in the United States for selected years, with the projection to $2020$.

$\begin{array}{ll}\text{Year}\hfill & \begin{array}{l}\text{National Expendirtures}\\ \text{for Health Car (billions)}\end{array}\hfill \\ 1960\hfill & \$28\hfill \\ 1970\hfill & 75\hfill \\ 1980\hfill & 254\hfill \\ 1990\hfill & 714\hfill \\ 1995\hfill & 1017\hfill \\ 2000\hfill & 1353\hfill \\ 2005\hfill & 1981\hfill \\ 2010\hfill & 2954\hfill \\ 2015\hfill & 3308\hfill \\ 2020\hfill & 4487\hfill \end{array}$

Use the scatter plot with $x$ as the number of years past $1950$ and $y$ as the total expenditures for the health care (in billions) to identify what type (or types) of function(s) would make a good model for these data.

Find a power model and a quadratic model for the data.

Which model from part (b) approximates more accurately the data point for $2020$.

Use the quadratic model to predict the $2025$ expenditures for national health care.