SOCIAL SCIENCE: Health Care ExpensesHealth care expenses in the United States have been gr...

SOCIAL SCIENCE: Health Care Expenses

Health care expenses in the United States have been growing rapidly for several decades. The following table gives per capita annual health care expenses for selected years.

a. Number the data columns with x-values 0–3 (so that x stands for the number of five-year intervals since 1990) and use exponential regression to fit a curve to the data. State the regression formula. [Hint: See Example 12 on pages 62–63.]

b. Use the regression function to predict annual health care expenses in the year 2015.

Source: U.S. Census Bureau, Statistical Abstract 2008

Example 12 EXPONENTIAL REGRESSION USING A GRAPHING CALCULATOR

In 2005 passengers flying on scheduled airlines worldwide flew a total of 2.41 trillion passenger-miles, which is equivalent to 5 million people flying to the moon and back in a year. The following graph shows the number of trillion passenger-miles flown in recent years.

Source: Worldwatch

a. Use exponential regression to fit a curve to the data and state the regression function.

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b. Use the regression function to predict world air travel in 2015.

Solution

a. We number the years with x-values 0–3, so x stands for the number of five-year intervals after 1990. We enter the data into lists, as shown in the first screen below (as explained in Graphing Calculator Basics— Entering Data on page xxiii), and use ZoomStat to graph the data points.

Then (using STAT, CALC, and ExpReg), we graph the regression along with the data points.

The regression curve, which fits the points quite well, is

y = 1.15 · 1.27x Rounded

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b. To predict sales in 2015, we evaluate Y1 at 5 (since x = 5 means 5 five-year intervals after 1990, giving 2015). From the screen on the right, if the current trend continues, airline flights worldwide will total about 3.8 trillion passenger-miles in 2015.