Question

Here is the actual tax table for 2022. This is how much you have to pay to the state of Arizona based on how much you make. If you make $26,500, you pay 2.59% of that income in taxes. If you make $26,600, you pay 2.59% on the bottom $26,500. You only pay 3.34% on the extra $100. This creates a piecewise function.

Can you write a function for this?
Calculate how much I owe in taxes if I made _______ in taxable income last year.
a. $50,000
b. $39.410
c. $1200
d. $181,475

Answer 1

If 2.69% of tax is paid when income is $26500 and 3.34% of the tax is paid on the greater amount to $26500 then the function which shows the tax amount is 0.0334x-198.75 in which x is the total income.

Given that 2.69% of tax is paid when income is $26500 and 3.34% of the tax is paid on the greater amount to $26500.

We are required to find the function which shows the tax amount and also calculate the tax amount at different incomes.

Let the income be x.

Tax=26500*2.59%+(x-26500)*3.34%

Tax=686.35+0.0334x-885.1

Tax=0.0334x-198.75

Now finding the tax on $50000,$39410,$1200 and $181475

Tax on $50000 income=10275*10%+31500*12%+8225*22%

=1027.5+3780+1809.5

=$6617

Tax on $39410=10275*10%+29135*12%

=1027.5+3496.2

=$4523.5

Tax on $1200=1200*10%

=$120

Tax on $181465=10275*10%+31500*12%+47300*22%+80975*24%

+11425*32%

=1027.5+3780+10406+19434+3656

=38303.5

Hence if 2.69% of tax is paid when income is $26500 and 3.34% of the tax is paid on the greater amount to $26500 then the function which shows the tax amount is 0.0334x-198.75 in which x is the total income.

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