In the United States, payroll taxes are levied to fund the Social Security Insurance and Medicare Insurance programs. The yearly tax is approximately as follows (though we will round off to make the calculations simpler):

(i) On all income, pay 1.5% toward Medicare Insurance.

(ii) Pay 6% on any income up to $100,00, toward Social Security Insurance.

(iii) Pay no additional tax toward Social Security, on any income beyond $100,000.

Yearly Income $$	Tax paid toward Medicare	Tax Paid toward Social Security	Total Tax Paid	Percentage of Income paid to Insurance
20,000	300	1200	1500	7.5
75,000	1125	4500	5625	7.5
100,000	1500	6000	7500	7.5%
A US Senator (**) see note below	1650	6000	7650	6.95%
500,000	7500	6000	13500	2.7%

If x is the income earned, write the piecewise formula for the total tax paid for these social insurance programs.

find a formula for P (x), the percentage tax a worker pays. Be sure to write this as a piecewise formula. Find limit as x > + for P (x).

Now draw a clearly labeled sketch of the function you found in (V). Be sure to indicate clearly the horizontal asymptote, based upon the work you did in (VI).