a. The combined taxes is represented by y and your total income is represented by x
Now, if the salary is greater than 102,000 social security is a fixed amount that is equal = 102,000*0.062 = 6,324. This is because you pay social security tax only on your first 102,000
The piece wise function is as follows:
y = 0.062*x +0.0145*x if x <=102,000
y = 6,324 + 0.0145*x if x>102,000
b. John's social security = 102,000*0.062 = $6,324 (Since you pay social security tax only on your first 102,000)
c. John's medicare tax = 0.0145*102,000 = $1,479
Let x be the income.
Let y be the combined taxes.
When [tex]x <102,000[/tex] then the income is less than maximum taxable income. Hence, we will pay social security tax on the whole income.
Social security tax = [tex]0.062\times x=0.062x[/tex]
When [tex]x\geq 102000[/tex] then we will pay social security on the maximum taxable income.
Social security tax = [tex]0.062\times102000=6324[/tex] dollars
Hence, Darby paid $6324 in Social Security tax.
Medicare tax will be = [tex]0.0145\times x=0.0145x[/tex]
So, Darby paid in medicare tax = [tex]0.0145\times143000=2073.50[/tex] dollars
Now combined tax or y = social security tax plus medicare tax
So, [tex]y=0.062x+0.0145x=0.0765x[/tex] when x<102000
and [tex]y=6324+0.0145x[/tex] when x≥102000
