Defense—Veteran Spending: A portion of the U.S. defense budget includes veterans’ outlays....

Defense—Veteran Spending: A portion of the U.S. defense budget includes veterans’ outlays. These outlays include budgets for veterans’ hospitals, educational scholarships, and disability payments. The annual outlays for U.S. veterans from 1990 to 2011 can be modeled by

 f(x) = 0.3x2 − 2.22x + 35.4 0 ≤ x ≤ 21

where x represents the number of years since 1990, and f(x) represents the veterans’ outlays in billions of dollars. The total annual Department of Defense budget during the same time period can be modeled by the function

 g(x) = 2.23x2 − 1.97x + 329.6 0 ≤ x ≤ 21

where x represents the number of years since 1990, and g(x) represents the annual U.S. defense budget in billions of dollars. (Source: U.S. Office of Management and Budget.)

(a) Evaluatef(11) and g(11), and interpret each of these values.

---

(b) Use the results of part (a) to compute . What does this percentage represent?

---

(c) Use your calculator to graph , and graph y3 in the viewing window [0, 21] by [0, 12]. Use the Minimum command on your graphing calculator to determine when the percentage of the U.S. defense budget allocated to veterans was at its lowest. What is the percentage?

Courtesy of Master Sgt. Ken Hammond, U.S. Air Force/U.S. Department of Defense