In a given year the U.S. federal income tax owed by a married couple filing jointly can be found from the following table:

(a) For incomes up to $137,300, 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 $50,000.
(d) A friend tells Jack Waddell not to earn any money over $68,000 because it would raise his tax rate to 25% on all of his taxable income. Test this statement by finding the tax due on $68,000 and 68,000 + $1. What do you conclude?

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Filing Status: Married Filing Jointly Of the If taxable income Tax due amount is is between $0 - $16,750 $16,750 – $68,000 $68,000 -– $137,300 $137,300 – $209,250 $209,250 – $373,650 $373,650 – Up over $0.00 + 10.0% 40 $1,675.00 + 15.0% $9,362.50 + 25.0% $26,687.50 + 28.0% $46,833.50 + 33.0% $101,085.50 + 35.0% $16,750 $68,000 $137,300 $209,250 $373,650