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A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function definition for T(x), the state income tax due on earnings of x dollars

bigguy1989  May 19, 2018
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T(x) =0 to $10,000 No tax

$10,000 to $19,999 1% tax

$20,000 to $39,999 2% tax

x - $40,000             3% tax

Example: Income of $100,000 will pay the following taxes:

On first $10,000 No tax

Next $10,000 will be taxed @ 1% = $100

Next $20,000 will be taxed @ 2% = $400. You add up the above 3 "brackets" : $10,000 + $10,000 + $20,000 =$40,000 on which you have already paid [$100 + $400] =$500 in taxes so far. Then:

$100,000 - $40,000 = $60,000 on which you will pay 3% tax. So:

$60,000 x 3% =$1,800 tax. So, the total tax on $100,000 income will be:

$100 + $400 + $1,800 =$2,300 tax that you will pay to the State.

Note: From this you can write your "multiline function definition of T(x)".

Guest May 19, 2018

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