Question

Mathematics for Data and Financial Literacy

Answer 1

Mathematics for Data and Financial Literacy

The piecewise function represents the amount of taxes owed, f(x), as a function of the taxable income, x. Use the marginal tax rate chart or the piecewise function to answer the questions.



Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%

A piecewise function f of x defined by seven pieces. Part 1 is 0.10x for 0 is less than x is less than or equal to 10,275. Part 2 is 0.12x minus 205.50 for 10,276 is less than or equal to x is less than or equal to 41,175. Part 3 is 0.22x minus 4,323 for 41,176 is less than or equal to x is less than or equal to 89,075. Part 4 is 0.24x minus 6,104.50 for 89,076 is less than or equal to x is less than or equal to 170,050. Part 5 is 0.32x minus 19,708.50 for 170,051 is less than or equal to x is less than or equal to 215,950. Part 6 is 035x minus 26,187 for 215,951 is less than or equal to x is less than or equal to 539,900. Part 7 is 0.37x minus 36,985 for x is greater than or equal to 539,901.

Part A: Using the method of your choice, demonstrate how to calculate the amount of taxes owed on a taxable income of $37,000. Show all work. (4 points)

Part B: Using the taxes owed from part A, determine the effective tax rate. Show all work. (4 points)

Part C: Compare the piecewise function to the marginal tax rate chart. How is the marginal tax rate chart represented in the piecewise function? (2 points)

Answer 2

holy shi this is a lot,

Answer 3

okay whatever

Answer 4

Part A: f(x) = 0.12 * 37,000 - 205.50 f(x) = 4,440 - 205.50 f(x) = $4,234. the amount of taxes owed is $4,234.50.

Answer 5

Effective tax rate = (4,234.50 / 37,000) * 100% Effective tax rate = 0.1145054 * 100% Effective tax rate ≈ 11.4the tax rate is 11.45%.

Answer 6

marginal tax rate chart both provide the same tax information, but the piecewise function presents it in a mathematical function form. Each part of the piecewise function corresponds to a specific tax bracket and provides a formula to calculate the taxes owed within that tax bracket. The marginal tax rate chart lists the tax brackets and their corresponding marginal tax rates.