Question

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 1

its a big one

Answer 2

i need the work also

Answer 3

Part A: To calculate the amount of taxes owed on a taxable income of $37,000, we need to find the tax bracket that includes $37,000. From the marginal tax rate chart, we can see that $37,000 falls in the third tax bracket, which has a marginal tax rate of 22%. Using the piecewise function, we can calculate the amount of taxes owed as follows:

f(x) = 0.22x - 4,323 for 41,176 ≤ x ≤ 89,075

f(37,000) = 0.22(37,000) - 4,323 = 2,827

Therefore, the amount of taxes owed on a taxable income of $37,000 is $2,827.

Part B: To determine the effective tax rate, we need to divide the amount of taxes owed by the taxable income. Using the taxes owed from Part A, we can calculate the effective tax rate as follows:

Effective tax rate = Taxes owed / Taxable income

Effective tax rate = 2,827 / 37,000

Effective tax rate = 0.0762 or 7.62%

Therefore, the effective tax rate for a taxable income of $37,000 is 7.62%.

Part C: The marginal tax rate chart is represented in the piecewise function by the different parts of the function that correspond to each tax bracket. Each part of the function has a different slope, which corresponds to the marginal tax rate for that tax bracket. The breakpoints between the different parts of the function correspond to the upper limits of each tax bracket. For example, the first part of the function (0.10x for 0 ≤ x ≤ 10,275) corresponds to the first tax bracket, which has a marginal tax rate of 10% and an upper limit of $10,275. The second part of the function (0.12x - 205.50 for 10,276 ≤ x ≤ 41,175) corresponds to the second tax bracket, which has a marginal tax rate of 12% and an upper limit of $41,175. And so on for the remaining tax brackets.

Answer 4

awsome, thank you :)

Answer 5

yww