SOLUTION: if you earned up to 5,000,000 in 2016 from an employer, your social security tax rate was 5.2% your income. if you earned over 5,000,000, you pay a fixed amount of 350000. a.write

Question 1167096: if you earned up to 5,000,000 in 2016 from an employer, your social security tax rate was 5.2% your income. if you earned over 5,000,000, you pay a fixed amount of 350000.
a.write a piecewise linear function to represent the social security taxes for incomes between 0 and 10,000,000.
b.how much social security tax would be deducted from someone who earns 250,000?
c.How much is your income if you paid 200,000 in social security tax in 2016?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your piecewise function is:

y = .052 * x for x <= 5,000,000

y = 350,000 for 5,000,000 < x <= 10,000,000

if you made 250,000, then the first formula would be used and your tax would .052 * 250,000 = 13,000.

if your income was 5,000,000,then your social security tax would be .052 * 5,000,000 = 260,000

since your social security tax is 200,000, then your income had to be less than 5,000,000.

your income is therefore 200,000 /.052 = 3,846,153.846.

this would be derived from the formula of y = .052 * x
when y = 200,000, the formula becomes 200,000 = .052 * x
solve for x to get x = 200,000 /.052 = 3,846,153.846.

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