Final answer:
The marginal tax rate is applied only to income within certain brackets, demonstrating a progressive tax system.
Step-by-step explanation:
The subject of this question is Mathematics, particularly related to the concept of piecewise functions in the context of federal income taxes. The marginal tax rate is a vital aspect of understanding how taxes are calculated, which can be explained through piecewise functions that model the progressive tax system in the United States.
To calculate the tax owed by someone with a taxable income of $20,000 using the given marginal tax rates, you would identify the appropriate tax bracket and apply the corresponding rate to compute the tax.
For instance, if the tax rate is 10% for income up to $9,075 and 15% for the income between $9,075 and $36,900, a person earning $20,000 would pay a base amount for the first bracket and an additional 15% on the income over $9,075. The tax calculation would be as follows: 837.50 + 0.15 × (20,000 - 9,075), resulting in a total tax of $2,581.25.
Understanding this concept helps in visualizing how income is taxed differently across various bands of earnings, generally leading to higher-income individuals paying a larger percentage of their marginal income as their earnings increase. This exemplifies a progressive tax system.