In a given year, the U.S. federal income tax owed by a married couple filing jointly can be found from the following table (Source: Internal Revenue Service, Form 1040 Instructions).

(a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned.

(b) Use the function to find T(70,000).

(c) Find the tax due on a taxable income of $100,000.

(d) A friend tells Jack Waddell not to earn any money over $75,300 because it will raise his tax rate to 25% on all of his taxable income. Test this statement by finding the tax due on $75,300 and $75,300 + $1. What do you conclude?

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Married Filing Jointly Taxable Income Tax Rate $0-$18,550 10% $1,855 plus 15% of the amount over $18,550 $18,551-$75,300 $75,301-$151,900 $10,367.50 plus 25% of the amount over $75,300 $151,901-$231,450 $29,517.50 plus 28% of the amount over $151,900 $231,451-$413,350 $51,791.50 plus 33% of the amount over $231,450 $413,351-$466,950 $111,818.50 plus 35% of the amount over $413,350 $466,951 or more $130,578.50 plus 39.6% of the amount over $466,950