Below are the instructions to calculate taxes due at the 2022 Tax Rate Schedule for people filing as "single" with a taxable income over $100,000. Let T(x) represent the taxes due for someone with a taxable income of x. Schedule A - Single Taxable income from line 15 At least $100,000 but not over $170,050 Over $170,050 but not over $215,950 Over (a) Enter the amount from line 15 (b) Multiplication amount 24% (0.24) 32% (0.32) 35% (0.35) $215,950 but not over $539,900 Over $539,900 1. Find T(160,000), T(200,000), T(400,000) and T(539,900.01). (c) Multiply (a) by (b) 37% (0.37) (d) Subtraction amount $6164.50 $19,768.50 $26,247.00 $37,045.00 (e) Tax Subtract (d) from (c). The result is the amount of tax due Let's explore what happens when individuals change tax brackets. 2. When the taxable income changes from just below 170,050 to just over 170,050, what happens to the tax amount? 3. When the taxable income changes from just below $215,950 to just above $215,950, what happens to the tax amount?
Below are the instructions to calculate taxes due at the 2022 Tax Rate Schedule for people filing as "single" with a taxable income over $100,000. Let T(x) represent the taxes due for someone with a taxable income of x. Schedule A - Single Taxable income from line 15 At least $100,000 but not over $170,050 Over $170,050 but not over $215,950 Over (a) Enter the amount from line 15 (b) Multiplication amount 24% (0.24) 32% (0.32) 35% (0.35) $215,950 but not over $539,900 Over $539,900 1. Find T(160,000), T(200,000), T(400,000) and T(539,900.01). (c) Multiply (a) by (b) 37% (0.37) (d) Subtraction amount $6164.50 $19,768.50 $26,247.00 $37,045.00 (e) Tax Subtract (d) from (c). The result is the amount of tax due Let's explore what happens when individuals change tax brackets. 2. When the taxable income changes from just below 170,050 to just over 170,050, what happens to the tax amount? 3. When the taxable income changes from just below $215,950 to just above $215,950, what happens to the tax amount?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Below are the instructions to calculate taxes due at the 2022 Tax Rate Schedule for people filing as "single" with a taxable income over $100,000. Let T(x) represent the taxes due for someone with a taxable income of x.
**Schedule A — Single**
| Taxable income from line 15 | (a) Enter the amount from line 15 | (b) Multiplication amount | (c) Multiply (a) by (b) | (d) Subtraction amount | (e) Tax Subtract (d) from (c). The result is the amount of tax due |
|------------------------------|----------------------------------|--------------------------|-------------------------|------------------------|------------------------------------------------------------------------|
| At least $100,000 but not over $170,050 | | 24% (0.24) | | $6,164.50 | |
| Over $170,050 but not over $215,950 | | 32% (0.32) | | $19,768.50 | |
| Over $215,950 but not over $539,900 | | 35% (0.35) | | $26,247.00 | |
| Over $539,900 | | 37% (0.37) | | $37,045.00 | |
1. Find T(160,000), T(200,000), T(400,000), and T(539,900.01).
Let's explore what happens when individuals change tax brackets.
2. When the taxable income changes from just below $170,050 to just over $170,050, what happens to the tax amount?
3. When the taxable income changes from just below $215,950 to just above $215,950, what happens to the tax amount?
![### Taxation and Piecewise Functions
This document delves into several taxation-related mathematical questions and provides a piecewise function for taxable income calculations.
#### Questions and Problems
3. **Taxable Income Transition**
*Question:* When the taxable income changes from just below $215,950 to just above $215,950, what happens to the tax amount?
4. **Impact of a Raise on Take-home Income**
*Question:* Is it possible that a raise at work can leave you with less take-home income?
5. **Function Verification**
*Question:* Is T(x) a function? Explain your reasoning.
6. **Piecewise Function for Tax Calculation**
*Task:* Express T(x) as a piecewise defined function. (I’ve started the notation for you.)
\[
T(x) =
\begin{cases}
100,000 < x \leq 170,050 \\
0.37x - 37045 & \text{if } 170,050 < x \leq
\end{cases}
\]
#### Explanation
- **Piecewise Function:**
The function T(x) is partially defined. It indicates that for taxable income within certain ranges, different calculations apply. More details might need to fill in the intervals or rules missing for complete understanding.
The provided questions explore the nuanced relationship between income changes and taxation, prompting an examination of whether salary increases might paradoxically reduce take-home pay due to tax bracket shifts. Additionally, it examines the concept of functions within these calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79384b4f-f6f5-4976-8d61-12e63a60eeb0%2F7b51ea6a-3fb3-4776-a201-d31251dea9c5%2Fky5qnyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Taxation and Piecewise Functions
This document delves into several taxation-related mathematical questions and provides a piecewise function for taxable income calculations.
#### Questions and Problems
3. **Taxable Income Transition**
*Question:* When the taxable income changes from just below $215,950 to just above $215,950, what happens to the tax amount?
4. **Impact of a Raise on Take-home Income**
*Question:* Is it possible that a raise at work can leave you with less take-home income?
5. **Function Verification**
*Question:* Is T(x) a function? Explain your reasoning.
6. **Piecewise Function for Tax Calculation**
*Task:* Express T(x) as a piecewise defined function. (I’ve started the notation for you.)
\[
T(x) =
\begin{cases}
100,000 < x \leq 170,050 \\
0.37x - 37045 & \text{if } 170,050 < x \leq
\end{cases}
\]
#### Explanation
- **Piecewise Function:**
The function T(x) is partially defined. It indicates that for taxable income within certain ranges, different calculations apply. More details might need to fill in the intervals or rules missing for complete understanding.
The provided questions explore the nuanced relationship between income changes and taxation, prompting an examination of whether salary increases might paradoxically reduce take-home pay due to tax bracket shifts. Additionally, it examines the concept of functions within these calculations.
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