For this assignment we will be looking at personal income taxes. In 2017 it was normal to be able to have deductions and a personal exemption deducted from ones total income before determining their taxable income. For the purposes of this activity, we will consider only a single filing status.

In 2017, the standard deduction was $6,350 and the personal exemption was $4,050. So, an individual who brought in a total income of $30,000 would have to pay taxes on $19,600 ($30,000-$6,350-$4050). The $19,600 represents their taxable income.

Part 1: Hypothetical Tax Code 1

Consider a simplified version of the real tax code. Assume that the tax rate on all taxable income is 15% and the standard deduction ($6,350) and personal exemption ($4,050) still apply.

1. If your total income before exemptions was $35,000, what is your taxable income?
2. How much would you have to pay in taxes on this income?
3. What percentage of your total income would you pay in taxes?
4. Write a function to model the total tax paid, T(x), with a total income of x dollars.
5. How many different slopes are on this graph (below)? What do they represent?

Below a graph that shows taxes paid as a function of total income for the total income between $0 and $60,000:

Part 2: Hypothetical Tax Code 2:

Now consider another hypothetical tax code. Assume the tax rate on the first $15,000 of taxable income is 10% and the tax rate on any additional income is 18%. The standard deduction ($6,350) and personal exemption ($4,050) still apply.

In other words:

For taxable income from $0 to $15,000, you pay 10% of your taxable income in taxes, plus For taxable income above $15,000, you pay 18% of your taxable income.

1. If your total income before exemptions were $10,000 how much would you pay in taxes?

2. If your total income were $20,000 how much would you pay in taxes?

3. If your total income were $50,000 how much would you pay in taxes?

4. Write a function to model the total tax paid, T(x), with a total income of x dollars.

5. Create a graph that shows taxes paid as a function of total income for the total income between $0 and $60,000.

6. How many different slopes are on this graph?

NOTE: For a Total Income of $80,000, an individual would pay $11,328 in taxes.

Part 3: House Tax Plan for 2018

For 2017 the actual tax brackets for a single tax filer were:

For taxable income from $0 to $9,325, you pay 10% of it in taxes, plus For taxable income from $9,326 to $37,950, you pay 15% of it in taxes, plus For taxable income from $37,951 to $91,900, you pay 25% of it in taxes, plus For taxable income from $91,901 to $191,650, you pay 28% of it in taxes, plus For taxable income from $191,651 to $416,700, you pay 33% of it in taxes, plus For taxable income from $416,701 to $418,400, you pay 35% of it in taxes, plus For taxable income at or above $418,401, you pay 39.6%.

At the end of 2017, the House proposed a new tax plan: (http://www.businessinsider.com/tax-brackets-2018-trump-tax-plan-chart-house-senate-comparison-2017-11)

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	Upper Bound	Rate	Maximum Money in Bracket	Maximum Tax in Bracket
   $0	$45,000	12%		$5,400
   $45,000			$155,000
   $200,000				$105,000
   	No Limit		No Limit	No Limit
   Total Income
   Lower Bound	Upper Bound	Rate	Maximum Money in Bracket	Maximum Tax in Bracket
   $0	$12,200	0%	$12,200	$0
   	$57,200		$45,000
   				$38,750
   $512,200	No Limit		No Limit	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.
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?

NOTE: For a Total Income of $85,000, an individual would pay $12,350 in taxes.