The following table shows the total national expenditures for health (in billions of dollars) for selected years from 2002 and projected to 2024. (These data include expenditures for medical research and medical facilities construction.)

Assume that these data can be modeled with the function
A(t) = 333(0.1t + 1)³ - 1830(0.1t + 1)² + 4510(0.1t + 1) - 1750
where A(t) is in billions of dollars and t is the number of years after 2000.

(a) Find the function that models the instantaneous rate of change of total national health care expenditures.

(b) Use the model from part (a) to find and interpret the instantaneous rate of change of national health care expenditures in 2012 and 2020.

(c) Use the data to find an average rate of change from 2018 to 2022 that approximates the instantaneous rate of change for 2020.

Transcribed Image Text:

Year Amount Year Amount 2002 1602 2014 3080 2004 1855 2016 3403 2006 2113 2018 3786 2008 2414 2020 4274 2010 2604 2022 4825 2012 2817 2024 5425