In a given year, the U.S. 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 T(x) = $18,551-$75,300 Tax Rate 10% $1,855 plus 15% of the amount over $18,550 $75,301-$151,900 amount over $75,300 $466,951 or more (a) For incomes up to $151,900, $10,367.50 plus 25% of the $29,517.50 plus 28% of the $151,901-$231,450 amount over $151,900 $51,791.50 plus 33% of the $231,451-$413,350 amount over $231,450 if $413,351-$466,950 amount over $413,350 $111,818.50 plus 35% of the $130,578.50 plus 39.6% of the amount over $466,950 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. 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find 7(40,000). (c) Find the tax due on a taxable income of $90,000. $ (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%.
In a given year, the U.S. 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 T(x) = $18,551-$75,300 Tax Rate 10% $1,855 plus 15% of the amount over $18,550 $75,301-$151,900 amount over $75,300 $466,951 or more (a) For incomes up to $151,900, $10,367.50 plus 25% of the $29,517.50 plus 28% of the $151,901-$231,450 amount over $151,900 $51,791.50 plus 33% of the $231,451-$413,350 amount over $231,450 if $413,351-$466,950 amount over $413,350 $111,818.50 plus 35% of the $130,578.50 plus 39.6% of the amount over $466,950 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. 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find 7(40,000). (c) Find the tax due on a taxable income of $90,000. $ (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%.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:In a given year, the U.S. 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
T(x) =
$18,551-$75,300
$75,301-$151,900 amount over $75,300
$413,351-$466,950
Tax Rate
10%
$1,855 plus 15% of the
amount over $18,550
$10,367.50 plus 25% of the
$151,901-$231,450 amount over $151,900
$466,951 or more
if
$29,517.50 plus 28% of the
$231,451-$413,350 amount over $231,450
$51,791.50 plus 33% of the
$130,578.50 plus 39.6% of
the amount over $466,950
(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.
$111,818.50 plus 35% of the
amount over $413,350
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 inco of $90,000.
$
(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?
O Jack's friend is correct, his entire encome is taxed at 25%.
o Jack's friend is wrong, only his income above $75,300 is taxed at 25%.
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