Transportation—Highway Construction: Federal highway spending is funded mainly through gas...

Transportation—Highway Construction: Federal highway spending is funded mainly through gas and other fuel taxes that are paid into the Highway Trust Fund. The annual receipts into the Highway Trust Fund from 1990 to 2011 can be modeled by the function

 f(x) = 0.24x2 + 1.92x + 77.86 0 ≤ x ≤ 21

where x represents the number of years since 1990, and f(x) represents the annual receipts into the Highway Trust Fund in billions of dollars. Conversely, the annual outlays from the Highway Trust Fund from 1990 to 2011 can be modeled by the function

 g(x) = 0.15x2 + 3.06x + 75.29 0 ≤ x ≤ 21

where x represents the number of years since 1990, and f(x) represents the annual outlays from the Highway Trust Fund in billions of dollars. (Source: U.S. Federal Highway Administration.)

(a) Simplify the difference of functions (f − g). Interpret the meaning of this operation on functions.

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(b) Evaluate (f − g) ( 11) and interpret the result.