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.