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Question

The end-of-year assets of the Medicare Hospital Insurance Trust Fund (in billions of dollars) for the years 2006 through 2014 are shown. 2006: 305.4, 2007: 326.0, 2008: 321.3, 2009: 304,.2 2010: 271.9, 2011: 244.2, 2012: 220.4, 2013: 205.4, 2014: 197.3. (a) Use the regression capabilities of a graphing utility to find a model of the form $M=a t^{3}+b t^{2}+c t+d$ for the data. Let t=6 represent 2006. (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.

Solution

VerifiedStep 1

1 of 4#### a)

$M(t)=0.995 t^{3}-31.26 t^{2}+297.3 t-566.9$

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