(a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned T(x) = the amount over $466,950 if 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find T(40,000). $ (c) Find the tax due on a taxable income of $100,000. $ (d) A friend tells Jack Waddell not to earn any money over $75,300 because it will raise his tax rate to 25% on all of his taxable income. Test this statement by finding the tax due on $75,300 and $75, T(75,300) = $ T(75,301) = $ What do you conclude? Jack's friend is correct, his entire encome is taxed at 25%. Jack's friend is wrong, only his income above $75,300 is taxed at 25%.
(a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned T(x) = the amount over $466,950 if 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find T(40,000). $ (c) Find the tax due on a taxable income of $100,000. $ (d) A friend tells Jack Waddell not to earn any money over $75,300 because it will raise his tax rate to 25% on all of his taxable income. Test this statement by finding the tax due on $75,300 and $75, T(75,300) = $ T(75,301) = $ What do you conclude? Jack's friend is correct, his entire encome is taxed at 25%. Jack's friend is wrong, only his income above $75,300 is taxed at 25%.
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.58TI: What is the total effect on the economy of a government tax rebate of $500 to each household in...
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Transcribed Image Text:Federal Income tax owed by a married couple filing jointly can be found from the following table.
Married Filing Jointly
Taxable Income
$0-$18,550
$18,551-$75,300
$75,301-$151,900
$151,901-$231,450
T(x) =
$231,451-$413,350
$413,351-$466,950
$466,951 or more
10%
if
Tax Rate
$1,855 plus 15% of the
amount over $18,550
$10,367.50 plus 25% of the
amount over $75,300
$29,517.50 plus 28% of the
amount over $151,900
$51,791.50 plus 33% of the
amount over $231,450
$111,818.50 plus 35% of the
amount over $413,350
(a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned
$130,578.50 plus 39.6% of
the amount over $466,950
0 < x≤ 18,550
if 18,550 < x≤ 75,300
(b) Use the function to find T(40,000).
$
if 75,300 < x≤ 151,900
(c) Find the tax due on a taxable income of $100,000.
$
(d) A friend tells Jack Waddell not to earn any money over $75,300 because it will raise his tax rate to 25% on all of his taxable income. Test this statement by finding the tax due on $75,300 and $75,300 - $1.
T(75,300) = $
T(75,301) = $
What do you conclude?
Jack's friend is correct, his entire encome is taxed at 25%.
Jack's friend is wrong, only his income above $75,300 is taxed at 25%.
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