Modeling Data The end-of-year assets of the Medicare Hospital Insurance Trust Fund (in

Chapter 4, Problem 96

(choose chapter or problem)

Modeling Data The end-of-year assets of the Medicare Hospital Insurance Trust Fund (in billions of dollars) for the years 1999 through 2010 are shown.

1999: 141.4; 2000: 177.5; 2001: 208.7; 2002: 234.8;

2003: 256.0; 2004: 269.3; 2005: 285.8; 2006: 305.4

2007: 326.0; 2008: 321.3; 2009: 304.2; 2010: 271.9

(Source: U.S. Centers for Medicare and Medicaid Services)

(a) Use the regression capabilities of a graphing utility to find a model of the form \(M=a t^{4}+b t^{3}+c t^{2}+d t+e\) for the data. (Let t= 9 represent 1999.)

(b) Use a graphing utility to plot the data and graph the model.

(c) Find the maximum value of the model and compare the result with the actual data.

Text Transcription:

M=a t^4+bt^3+c t^2+dt+e

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