Refer to Exercise.
(a) Find a formula for T (x) for all taxable income x.
(b) Plot T (x).
(c) Determine the maximum amount of tax that you will pay on the portion of your income in the fourth tax bracket.
Computing Income Tax The tax that you pay to the federal government is a percentage of your taxable income, which is what remains of your gross income after you subtract your allowed deductions. In a recent year, there were five rates or brackets for a single taxpayer, as shown in Table 1.
TABLE 1 Single Taxpayer Rates
Amount Over | But Not Over | Tax Rate |
$0 | $27,050 | 15% |
$27,050 | $65,550 | 27.5% |
$65,550 | $136,750 | 30.5% |
$136,750 | $297,350 | 35.5% |
$297,350 |
| 39.1% |
So, if you are single and your taxable income was less than $27,050, your tax is your taxable income times 15% (.15). The maximum amount of tax that you will pay on your income in this first bracket is 15% of $27,050, or (.15) × 27,050 = 4057.50 dollars. If your taxable income is more than $27,050 but less than $65,550, your tax is $4057.50 plus 27.5% of the amount in excess of $27,050. So, for example, if your taxable income is $50,000, your tax is $4057.5 + .275(50,000 − 27,050) = 4057.5 + .275 × 22,950 = $10,368.75. Let x denote your taxable income and T (x) your tax.
(a) Find a formula for T (x) if x is not over $136,750.
(b) Plot the graph of T (x) for 0 ≤ x ≤ 136,750.
(c) Find the maximum amount of tax that you will pay on the portion of your income in the second tax bracket. Express this amount as a difference between two values of T (x).
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.