Calculus

New York state income tax is based on taxable income which is part of a person's total income. The tax owed to the state is calculated using taxable income (not total income). In 2005, for a single person with a taxable income between $20,000 and $100,000, the tax owed was $973 plus 6.85% of the taxable income over $20,000. Answer the following questions, and DO NOT include any commas in your final answers.
(a) Compute the tax owed by a person whose taxable income is $81,000.
tax = $ (round to nearest dollar)

(b) Consider a lawyer whose taxable income is 90% of her total income, $x, where x is between $60,000 and $120,000. Write a formula for T(x), the amount of taxable income (not the tax owed, yet).
T(x) =

(c) Write a formula for L(x), the amount owed by the lawyer in part (b).
L(x) =

(d) Use L(x) to evaluate the tax liability (amount owed) for x = 90 ,000 and compare your results to part (a).
L( 90000 ) = $ (round to nearest dollar)

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  1. a) 973 + .0685 ( 81000 - 20000)

    b) T = .9 x

    c) L = 973 + .0685 (.9 x - 20000)

    d) 973 + .0685 (.9*90000 - 20000) same as a above

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