The federal income tax (as of 2014) has seven tax brackets, ranging from 10% to

Question

The federal income tax (as of 2014) has seven tax brackets, ranging from 10% to 39.6% of taxable income. But even if you are in a high tax bracket, not all of your income is taxed at that percent. The first $9075 of your income would be taxed at 10%, the next interval at 15%, then 25%, etc. Let’s devise a simpler plan: 15% on the first $90,000 of taxable income and 30% on all income above $90,000.
a. Let a denote taxable income and let T(a) be the tax on that income. Find a piecewise formula for T(a). Be sure to define what interval of the domain each “piece” is for. Write an appropriate IF statement.

Explanation / Answer

Solution : The making of piecewise formula for taxable income is quite simple, we just have to move according to the given conditions.So,

IF a<90000 THEN T(a) = a*0.15
ELSE T(a) = 90000*0.15 + (a - 90000)*0.30

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