Chapter 2.3, Problem 82AYU

National Debt The size of the total debt owed by the United States federal government continues to grow. In fact, according to the Department of the Treasury, the debt per person living in the United States is approximately $\$63,720$(or over $\$172,000$ per U.S. household). The following data represent the U.S. debt for the years $2007-2017$. Since the debt $D$ depends on the year $y,$ and each input corresponds to exactly one output, the debt is a function of the year. So $D(y)$ represents the debt for each year $y.$

$\begin{array}{cc}\text{Year}& \text{Debt(billions}\text{of}\text{dollars)}\\ 2007& 9008\\ 2008& 10,025\\ 2009& 11,910\\ 2010& 13,562\\ 2011& 14,790\\ 2012& 16,066\\ 2013& 16,738\\ 2014& 17,824\\ 2015& 18,151\\ 2016& 19,573\\ 2017& 20,245\end{array}$

Plot the points $(2007,9008),(2008,10025)$, and so on.

Draw a line segment from the point $(2007,9008)$ to $(2012,16066)$. What does the slope of this line segment represent?

Find the average rate of change of the debt from $2008$ to $2010$.

Find the average rate of change of the debt from $2011$ to $2013$.

Find the average rate of change of the debt from $2014$ to $2016$.

What appears to be happening to the average rate of change as time passes?