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(1) To ensure that you understand the system, fill in the following table. Tax Paid toward Social Security Total Tax Paid Percentage of Income paid

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(1) To ensure that you understand the system, fill in the following table. Tax Paid toward Social Security Total Tax Paid Percentage of Income paid to Insurance Yearly Income Tax paid $$ toward Medicare 20,000 75,000 100,000 110,000 500,000 (II) If x is the income earned, write the piecewise formula for the total tax paid for these social insurance programs. (III) Make a graph of (II). (IV) Use (III) to find the income one would pay if his total tax is (a) $6000; (b) $10,000; (V) Next, use your answer from (II) to find a formula for P(x), the percentage tax a worker pays. (V) Show that your formula in (V) matches the answers you found in the table above. for P(x). (VI) Now find the limit as x++ (VII) Finally, explain why your answer to (VI) makes total sense. That is, why could you have predicted the percentage paid by a billionaire without doing any calculations? (1) To ensure that you understand the system, fill in the following table. Tax Paid toward Social Security Total Tax Paid Percentage of Income paid to Insurance Yearly Income Tax paid $$ toward Medicare 20,000 75,000 100,000 110,000 500,000 (II) If x is the income earned, write the piecewise formula for the total tax paid for these social insurance programs. (III) Make a graph of (II). (IV) Use (III) to find the income one would pay if his total tax is (a) $6000; (b) $10,000; (V) Next, use your answer from (II) to find a formula for P(x), the percentage tax a worker pays. (V) Show that your formula in (V) matches the answers you found in the table above. for P(x). (VI) Now find the limit as x++ (VII) Finally, explain why your answer to (VI) makes total sense. That is, why could you have predicted the percentage paid by a billionaire without doing any calculations

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