Canadian federal income tax works on a graduated system, meaning the amount that you pay depends on your income. Within each tax bracket, you only pay the income tax rate on the amount of your income that falls within that range. For example, if you earn $50,000, then you pay 15% on the first $48,535 and 20.5% on the remaining $1,465. The 2020 Canadian federal income tax rates are shown below: 2020 Federal Income Tax Bracket 2020 Federal Income Tax Rate $48,535 or less more than $48,535 and up to $97,069 more than $97,069 and up to $150,473 more than $150,473 and up to $214,368 More than $214,368 15% 20.5% 26% 29% 33% Table 1: Canadian federal tax rates Let T(x) represent the amount of income tax (in dollars) that a Canadian person paid in 2020 based on their income, x (in dollars). (a) Based on the information in the table, T(x) is a piecewise defined function of the form: 0.15x if x < 48, 535 0.205(x – 48535) + 7280.25 if 48, 535 < x < 97,069 T(x) : if 97, 069 < x < 150, 473 if 150, 473 < x < 214, 368 if 214, 368 < x Fill in the rest of the definition of T(x) as a piecewise defined function. Explain briefly how the expressions. you determined (b) If the CEO of company NewldeasStartup earned $162,000 in 2020, how much federal tax did they have to рay? (c) Use your answer to part (a) to determine whether T(x) is continuous for all æ E (0, 0). Show your work.
Canadian federal income tax works on a graduated system, meaning the amount that you pay depends on your income. Within each tax bracket, you only pay the income tax rate on the amount of your income that falls within that range. For example, if you earn $50,000, then you pay 15% on the first $48,535 and 20.5% on the remaining $1,465. The 2020 Canadian federal income tax rates are shown below: 2020 Federal Income Tax Bracket 2020 Federal Income Tax Rate $48,535 or less more than $48,535 and up to $97,069 more than $97,069 and up to $150,473 more than $150,473 and up to $214,368 More than $214,368 15% 20.5% 26% 29% 33% Table 1: Canadian federal tax rates Let T(x) represent the amount of income tax (in dollars) that a Canadian person paid in 2020 based on their income, x (in dollars). (a) Based on the information in the table, T(x) is a piecewise defined function of the form: 0.15x if x < 48, 535 0.205(x – 48535) + 7280.25 if 48, 535 < x < 97,069 T(x) : if 97, 069 < x < 150, 473 if 150, 473 < x < 214, 368 if 214, 368 < x Fill in the rest of the definition of T(x) as a piecewise defined function. Explain briefly how the expressions. you determined (b) If the CEO of company NewldeasStartup earned $162,000 in 2020, how much federal tax did they have to рay? (c) Use your answer to part (a) to determine whether T(x) is continuous for all æ E (0, 0). Show your work.
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:1. Canadian federal income tax works on a graduated system, meaning the amount that you pay depends on your
income. Within each tax bracket, you only pay the income tax rate on the amount of your income that falls within
that range. For example, if you earn $50,000, then you pay 15% on the first $48,535 and 20.5% on the remaining
$1,465. The 2020 Canadian federal income tax rates are shown below:
2020 Federal Income Tax Bracket
2020 Federal Income Tax Rate
15%
$48,535 or less
more than $48,535 and up to $97,069
more than $97,069 and up to $150,473
more than $150,473 and up to $214,368
More than $214,368
20.5%
26%
29%
33%
Table 1: Canadian federal tax rates
Let T(x) represent the amount of income tax (in dollars) that a Canadian person paid in 2020 based on their
income, x (in dollars).
(a) Based on the information in the table, T(x) is a piecewise defined function of the form:
0.15x
if x < 48, 535
0.205(x – 48535)+ 7280.25 if 48, 535 < x < 97,069
T(x) =
if 97, 069 < x < 150, 473
if 150, 473 < х< 214, 368
if 214, 368 < x
Fill in the rest of the definition of T(x) as a piecewise defined function. Explain briefly how you determined
the expressions.
(b) If the CEO of company NewldeasStartup earned $162,000 in 2020, how much federal tax did they have to
рay?
(c) Use your answer to part (a) to determine whether T(x) is continuous for all x E (0, 0). Show your work.
(d) A UTM student on an internship at NewldeasStartup was supposed to earn $48,000, but after some extra
hard work, the company paid the student $49,000. Was there a large change in the tax paid? Did the student
lose money or earn more after tax, due to the additional pay?
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