To interpret the tax rates for a client earning $54,000 based on a piecewise linear function, it's important to understand how income tax brackets work.
Typically, income is taxed at different rates for different portions of that income. Based on your description, let’s break down how taxes would apply to a $54,000 income:
- First Tax Bracket: The client will be taxed at 10% for the first $9,275 of taxable income.
- Second Tax Bracket: The client will be taxed at 15% for the next amount up to $37,650. This means the client is taxed at 15% for the income between $9,276 and $37,650.
- Third Tax Bracket: The client will be taxed at 25% on the amount over $37,650. This applies to the income over $37,650.
Let's calculate the portions:
- 10% taxed on: $9,275 → $927.50
- 15% taxed on: $37,650 - $9,275 = $28,375 → $4,256.25
- 25% taxed on: $54,000 - $37,650 = $16,350 → $4,087.50
Thus, the best interpretation of the tax situation for the client earning $54,000 is:
"The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $28,375, which is the amount of taxable income within the second step. The remaining $16,350 will be taxed at a rate of 25%."
This option accurately describes how the taxes will be calculated based on the provided income and the different tax brackets.
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