Explanation Definition: Mathematical model describing a data is a function that which should get satisfied for all the values of the data and a linear model describing a data is a function of first degree of the form f x = m x + b such that the change in f x for every interval is the same provided the intervals of x are equally spaced. Calculation: Given, The data Taxable income Tax 72, 000 9911 72, 200 9941 72, 400 9971 72, 600 10, 014 72, 800 10, 064 73, 000 10, 114 73, 200 10, 164 73, 400 10, 214 73, 600 10, 264 73, 800 10, 314 74, 000 10, 364 74, 200 10, 414 Construct the table of difference for the above data. Change in income ( $ ) Change in tax ( $ ) From 72, 000 to 72, 200 30 From 72, 200 to 72, 400 30 From 72, 400 to 72, 600 30 From 72, 600 to 72, 800 43 From 72, 800 to 73, 000 50 From 73, 000 to 73, 200 50 From 73, 200 to 73, 400 50 From 73, 400 to 73, 600 50 From 73, 600 to 73, 800 50 From 73, 800 to 74, 000 50 From 74, 000 to 74, 200 50 From the above table, the difference of the tax is same for the amounts from $ 72 , 000 to $ 72 , 600 and also for the amount from $ 72 , 800 to $ 74 , 200 . Hence, in the given table, the part of the table starting from the amount $ 72 , 000 to $ 72 , 600 is linear and also the part starting from the amount $ 72 , 800 to $ 74 , 200 is linear. Now, let us find the formula for linear function of the first part of the table. (i.e.) The taxable income starting from $ 72 , 000 to $ 72 , 600 . Let ‘ I ’ denotes the taxable income and ‘ t ’ denotes the corresponding tax. From the difference table constructed, we have Change in function = Change in ‘ t ’ = 30 Change in variable = Change in ‘ I ’ = 200 Now, the slope is given by the formula S l o p e = C h a n g e i n f u n c t i o n C h a n g e i n v a r i a b l e = C h a n g e i n ' t ' C h a n g e i n ' I ' = 30 200 Slope = 0.15 Let the linear model be t = m I + b t = 0.15 I + b Take I = 72 , 000 and t = 9911 9911 = 0.15 72 , 000 + b 9911 = 10 , 800 + b Add - 10 , 800 on both sides 9911 - 10 , 800 = 10 , 800 + b - 10 , 800 - 889 = b (i To determine (b). To compare: The answer to part a with the answer to Exercise-18. To determine (c). To investigate: The tax law and to discover the determination of transition level and also to explain the meaning of bracket creep.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN: 9781337111348

Author: Bruce Crauder, Benny Evans, Alan Noell

Publisher: Cengage Learning

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Chapter 3.3, Problem 22E

To determine

(a)

To find:

The part of the table that represents linear function there by to find formulas for both linear functions.

To determine

(b). To compare:

The answer to part a with the answer to Exercise-18.

To determine

(c). To investigate:

The tax law and to discover the determination of transition level and also to explain the meaning of bracket creep.

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Chapter 3.3, Problem 21E

Chapter 3.3, Problem 23E

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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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(a) To find: The part of the table that represents linear function there by to find formulas for both linear functions.

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(a) To find: The part of the table that represents linear function there by to find formulas for both linear functions.

(b). To compare: The answer to part a with the answer to Exercise-18.

(c). To investigate: The tax law and to discover the determination of transition level and also to explain the meaning of bracket creep.

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Chapter 3 Solutions

(a)

To find:

The part of the table that represents linear function there by to find formulas for both linear functions.

(b). To compare:

The answer to part a with the answer to Exercise-18.

(c). To investigate:

The tax law and to discover the determination of transition level and also to explain the meaning of bracket creep.