U.S. military expenditures: Except for the year 1991 when military spending was cut drastically, the amount spent by the U.S. government on national defense and veterans’ benefits rose steadily from 1980 to 1992. These expenditures can be modeled by the function S(t) = −1.35t2 + 31.9t + 152, where S(t) is in billions of dollars and 1980 corresponds to t = 0.
From 1992 to 1996 this spending declined, then began to rise in the following years. From 1992 to 2002, military-related spending can be modeled by S(t) = 2.5t2 − 80.6t + 950.
Source: 2004 Statistical Abstract of the United States, Table 492
(a) Write S(t) as a single piecewise-defined function. Include stating the domain for each piece. Then (b) sketch the graph and use the function to estimate the amount spent by the United States in 2005, 2008, and 2012 if this trend continues.
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