The amount of income tax, t, an individual owes is defined by piecewise function () and is based on the individual's income, where / is taxable income in dollars. 0.12/ t(i)= 655+0.13(i-14000) 4500+ b(i-40000) if 0 si≤ 15,000 if 15,000 37,000 Part A: Show that the function t(i) is not continuous at /= 15,000. Part B: Find the value of constant that makes t() continuous at /= 37,000.1
The amount of income tax, t, an individual owes is defined by piecewise function () and is based on the individual's income, where / is taxable income in dollars. 0.12/ t(i)= 655+0.13(i-14000) 4500+ b(i-40000) if 0 si≤ 15,000 if 15,000 37,000 Part A: Show that the function t(i) is not continuous at /= 15,000. Part B: Find the value of constant that makes t() continuous at /= 37,000.1
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 88E
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![The amount of income tax, t, an individual owes is defined by piecewise function t(i) and is based on the individual's income, where iis taxable income in dollars.
t(i) =
0.12i
655+0.13(i-14000)
4500+ b(i-40000)
if 0 ≤ i ≤ 15,000
if 15,000<i≤ 37,000
if i > 37,000
Part A: Show that the function t(i) is not continuous at /= 15,000.
Part B: Find the value of constant b that makes (1) continuous at /= 37,000.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9b1d45f-2625-4b93-b570-df748e06f675%2F4cdb7ec3-bf3e-4e84-a2e2-098201bd4063%2Fzz37sfl_processed.png&w=3840&q=75)
Transcribed Image Text:The amount of income tax, t, an individual owes is defined by piecewise function t(i) and is based on the individual's income, where iis taxable income in dollars.
t(i) =
0.12i
655+0.13(i-14000)
4500+ b(i-40000)
if 0 ≤ i ≤ 15,000
if 15,000<i≤ 37,000
if i > 37,000
Part A: Show that the function t(i) is not continuous at /= 15,000.
Part B: Find the value of constant b that makes (1) continuous at /= 37,000.
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