Question

The state of Alaska has only two income tax brackets. Income up to $5000 is taxed at a rate of 5%. Income in excess of $5000 is taxed at a rate of 15%. Write a formula for the total amount of tax, T(x), paid for an income x greater than 5000.

Answer 1

The formula for calculating the total amount of tax paid for an income greater than $5000 in Alaska is T(x) = 0.05 * (x - 5000) + 0.15 * (x - 5000). It calculates the tax for the income above $5000 at a rate of 5% and adds it to the tax for the income above $5000 at a rate of 15%.

Step-by-step explanation:

To calculate the total amount of tax, T(x), paid for an income x greater than $5000 in Alaska, we can use the following formula:

T(x) = 0.05 * (x - 5000) + 0.15 * (x - 5000)

This formula calculates the tax for the income above $5000 at a rate of 5% and adds it to the tax for the income above $5000 at a rate of 15%. By subtracting $5000 from the income, we ensure that only the amount above $5000 is taxed.

For example, if a person's income is $7000, the total amount of tax would be:

T(7000) = 0.05 * (7000 - 5000) + 0.15 * (7000 - 5000) = 0.05 * 2000 + 0.15 * 2000 = $100 + $300 = $400