Chapter 11.2, Problem 21Q

The growth of federal expenditures is one of the characteristic features of the U.S. economy. The rapidity of the increases from 2000 to 2015, as shown in the table below, suggests an exponential model.

Year	Years after 2000, $x$	Gross Federal Debt (in $ trillions), $y$
2000	0	5.629
2001	1	5.770
2002	2	6.198
2003	3	6.760
2004	4	7.355
2005	5	7.905
2006	6	8.451
2007	7	8.951
2008	8	9.986
2009	9	11.876
2010	10	13.529
2011	11	14.764
2012	12	16.051
2013	13	16.719
2014	14	17.794
2015	15	18.120

Source: http/www.whitehouse.gov/omb/budget/Historicals

• (a) Find the best-fitting exponential curve, using the method of least squares together with an appropriate linearizing transformation. Use the sums: ${\displaystyle \underset{i=0}{\overset{15}{\sum }}{x}_i}=120,{\displaystyle \underset{i=0}{\overset{15}{\sum }}\ln y_i}=37.04571$, and ${\displaystyle \underset{i=0}{\overset{15}{\sum }}{x}_i\cdot \ln y_i}=307.6275$

• (b) Calculate the residuals for the years 2009 through 2015. What does this say about the exponential model?