The dollars spent per person per year for health care (projected to 2018) are shown in the table. These data can be modeled by

where x is the number of years past 1990 and y is the per capita expenditures for health care.
(a) Find the instantaneous rate of change of per capita health care expenditures in 2005 and 2015.
(b) Interpret the rate of change for 2015 found in part (a).
(c) Use the data to find the average rate of change of per capita health care expenditures from 2004 to 2006. How well does this approximate the instantaneous rate of change in 2005?

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4.38(x y = – 10)? + 78(x – 10) 0.0029x + 0.25 + 1430 $ per Person 8465 9275 10,289 11,520 12,994 Year $ per Person Year 4789 5563 6331 7091 7826 2010 2012 2014 2016 2018 2000 2002 2004 2006 2008