Precalculus—Math 12
Project 1: Some Taxing Problems

Instructions:  Write your answers to the following questions on separate paper.  Answers should be written in complete sentences.  Use a full sheet of paper (graph paper, if you like) for #1.  Label all axes and indicate coordinates of significant points.

If the amount on Form 1040, line 40
is over:	but not over:	then the tax is	plus this % of the additional amount
$0	$7,000	…	10%
$7,000	$28,400	$700	15%
$28,400	$68,800	$3,910	25%
$68,800	$143,500	$14,010	28%
$143,500	$311,950	$34,926	33%
$311,950	…	$90,514.50	35%

 In the US, federal taxation rates depend on “income bracket.”  The idea behind income brackets is that people who earn less money should not have to spend as high a percent of their income on taxes.  A piecewise function can be used to determine the taxes paid based on someone’s annual income. 

 

In 2003, t he IRS used to use a function of the following form to determine T, the amount of taxes paid, based on I, annual taxable income.

 

1.      Sketch the graph of T = f(I) for .

Taxable Income	Taxes	Net Income
$10,000
$25,000
$30,000
$60,000
$70,000
$120,000
$150,000
$250,000
$350,000

2.      Use this taxation function to fill in the following table of taxes and net income vs. taxable income:

 

3.      Find a formula for the piecewise function f(I) which expresses federal income taxes T as a function of taxable income I.

 

4.      Find a formula for the piecewise function g(I) which expresses net income after taxes as a function of taxable income.

 

5.      Vice President Cheney earned $813,226 in 2003.  What percent of his income would he pay in federal taxes on that income?  Gov. Shwarzenegger earned $26,138,000 in 2003.  What percent of this income would he pay in federal taxes?