Chapter 9.7, Problem 45E

Per capita expenditures for U.S. health care The following table shows the amount spent per person for health care in the United States for selected years from 2002 and projected to 2024. These data can be modeled by

$y=\frac{4.6{\left(x+10\right)}^2-49\left(x+10\right)+1600}{0.0026x+0.28}$ where x is the number of years after 2000 and y is per capita expenditures for health care.

(a) Find the instantaneous rate of change of per capita health care expenditures (to the nearest dollar) for 2010 and 2020.

(b) Interpret the rate of change for 2020 found in part (a).

(c) Use the data to find the average rate of change from 2018 to 2020. How well does this approximate the rate of change in 2020?

Year	$ per Person	Year	$ per Person
2002	5563	2014	9695
2004	6331	2016	10,527
2006	7091	2018	11,499
2008	7944	2020	12,741
2010	8428	2022	14,129
2012	8996	2024	15,618

Source: U.S. Centers for Medicare and Medicaid Services