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.
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