The table shows the national health care expenditures h (in billions of dollars) in the United States and the population p (in millions) of the United States for the years 2008 through 2013. The year is represented by t, with t = 8 corresponding to 2008. (Source: U.S. Centers for Medicare & Medicaid Services and U.S. Census Bureau)

(a) Use a graphing utility to find linear models for the health care expenditures h(t) and the population p(t).

(b) Use a graphing utility to graph h(t) and p(t).

(c) Find A = h(t)p(t), then graph A using a graphing utility. What does this function represent?

(d) Find and interpret A′(t) in the context of the problem.

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Year, t h P 8 9 2414 2506 304 307 10 11 12 2604 2705 2817 309 311 313 13 2919 315