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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