Question

Proposed New Tax Plan:

. For taxable income from $0 to $45,000, you pay 12% of it in taxes, plus
• For taxable income from $45,001 to $200,000, you pay 25% of it in taxes, plus
• For taxable income from $200,001 to $500,000, you pay 35% of it in taxes, plus
. For taxable income of $500,001 or more, you pay 39.6%.
Where the standard deduction was raised to $12,200 and the personal exemption
was eliminated. For the remaining exercises, we will only consider this proposed tax
plan.
1. Complete both of the tables below:
Taxable Income
Lower Bound
$0
$45,000
$200,000
Total Income
Lower Bound
$0
Upper Bound
No Limit
$45,000
Upper Bound
$12,200
$57,200
Rate
12%
Rate
0%
Maximum
Money in
Bracket
$155,000
No Limit
Maximum
Money in
Bracket
$12,200
$45,000
No Limit
Maximum
Tax in
Bracket
$5,400
$105,000
No Limit
Maximum
Tax in
Bracket
$0
$38,750
$512,200 No Limit
2. How many slopes would be on this graph?
3. Write a function to model the total tax paid, T(x), with a total income of x dollars.
No Limit
4. How much does a person pay in taxes if their total income is $210,000?
5. What is the slope of the line when an individual's total income is $210,000?

Answer 1

Answer:. Complete both of the tables below:

Taxable Income:

- The lower bounds of the income brackets are $0, $45,000, and $200,000.

- The upper bounds for the income brackets are not specified, except for the highest bracket which has no limit.

- The rates for each income bracket are 12%, 25%, 35%, and 39.6% respectively.

- The maximum money in each bracket is $155,000, no limit, $12,200, $45,000, and no limit respectively.

- The maximum tax in each bracket is $5,400, $105,000, no limit, $38,750, and no limit respectively.

Total Income:

- The lower bounds of the income brackets are $0, $12,200, and $57,200.

- The upper bounds for the income brackets are not specified, except for the highest bracket which has no limit.

- The rates for each income bracket are 0%, 12%, and 25% respectively.

- The maximum money in each bracket is $12,200, $45,000, and no limit respectively.

- The maximum tax in each bracket is $0, $38,750, and no limit respectively.

2. The number of slopes on this graph would be three. Each income bracket represents a different slope.

3. To model the total tax paid, T(x), with a total income of x dollars, we can use the information given in the proposed tax plan. We will use the following formula:

- For taxable income from $0 to $45,000, T(x) = 0.12x

- For taxable income from $45,001 to $200,000, T(x) = 0.25x - $5,400

- For taxable income from $200,001 to $500,000, T(x) = 0.35x - $105,000

- For taxable income of $500,001 or more, T(x) = 0.396x - $155,000

4. If a person's total income is $210,000, we need to find the tax paid using the tax brackets. The income falls into the third bracket. Using the formula T(x) = 0.35x - $105,000, we can substitute x = $210,000 to calculate the tax paid:

T(210,000) = 0.35 * 210,000 - $105,000 = $73,500

5. The slope of the line when an individual's total income is $210,000 corresponds to the tax rate in the third bracket. From the given information, we know that the tax rate for the third bracket is 35%. Therefore, the slope of the line would be 35%.