The table gives the annual cost per person age 65 and older for home health care from 2006 and projected through 2021. While these annual costs per person may seem modest, the majorities of older Americans live healthy, active lives and require no special care.

(a) With t equal to the number of years past 2005, find a cubic function C(t) that models the annual cost per person age 65 and older for home health care. Report the model with three significant digits.

(b) Find the point of inflection of the reported model. Examine the function on either side of the point of inflection and interpret your results.

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Cost (in $)| Year Cost (in $) Year 1418 1967 2006 2014 2007 1529 2015 2045 2008 1589 2016 2122 2017 2009 1673 2203 2018 2010 1764 2305 2011 1787 2019 2416 2532 2012 1841 2020 2013 1883 2021 2653