The table shows the total national expenditures for health (both actual and projected, in billions of dollars) for the years from 2001 to 2018. (These data include expenditures for medical research and medical facilities construction.)

Assume these data can be modeled with the function
A(t) = 445(0.1t + 1)3 - 2120 (0.1t + 1)2 + 4570(0.1t + 1) - 1600
where A(t) is in billions of dollars and t is the number of years past 2000.
(a) Use this model to determine and interpret the instantaneous rates of change of the total national health expenditures in 2008 and 2015.
(b) Use the data to find an average rate of change that approximates the 2015 instantaneous rate.

Transcribed Image Text:

Year Amount Year Amount $1469 1602 $2624 2001 2010 2002 2011 2770 2003 1735 2012 2931 2013 2004 1855 3111 2005 1981 2014 3313 2015 2006 2113 3541 2241 2007 2016 3790 2008 2379 2017 4062 2018 2009 2509 4353