The table shows the numbers N (in millions) of students enrolled in elementary and secondary schools in

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The table shows the numbers N (in millions) of students enrolled in elementary and secondary schools in the United States from 2005 through 2014.
Number, N DATA Year 2005 49.11 2006 49.32 49.29 2007 2008 49.27 2009 49.36 2010 49.48 2011 49.52 2012 49.77 2013 49.94 2

(a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t = 5
corresponding to 2005.
(b) Use the regression feature of the graphing utility to find a quartic model for the data. (A quartic model has the form at4 + bt3 + ct2 + dt + e, where a, b, c, d, and e are constant and t is variable.)
(c) Graph the model and the scatter plot in the same viewing window. How well does the model fit the data?
(d) According to the model, after 2014, when did the number of students enrolled in elementary and secondary schools fall below 48 million?
(e) Is the model valid for long-term predictions of student enrollment? Explain.

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