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# im lost

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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

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)".

May 19, 2018