Federal income tax

Definition

Federal income tax is a tax levied by the United States government on the annual earnings of individuals, corporations, trusts, and other legal entities. It is calculated based on a progressive tax system with different rates applied to different income brackets.

5 Must Know Facts For Your Next Test

1. The federal income tax can be represented mathematically as an integral to calculate total taxes owed over an interval of income.
2. Integration formulas are used to determine the area under the curve of a tax rate function, representing total taxes paid.
3. The Net Change Theorem helps in finding the total change in taxes owed when there is a change in income over time.
4. Piecewise functions often represent federal income tax brackets where different integration rules apply for each segment.
5. Understanding continuous functions and their integrals can help estimate effective tax rates over varying incomes.

Review Questions

• How can integration be used to model the calculation of federal income tax?
• Explain how piecewise functions are relevant to understanding federal income tax brackets using integration techniques.
• Describe how the Net Change Theorem applies to changes in taxable income and corresponding taxes owed.

Related terms

Integral: A mathematical concept that represents the accumulation of quantities, often used to find areas under curves.

Net Change Theorem: A principle stating that the integral of a rate of change function over an interval gives the net change in the original function over that interval.

Piecewise Function: A function composed of multiple sub-functions, each defined on a certain interval, commonly used to represent federal income tax brackets.