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(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%.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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%.
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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