To explain the tax rates to a client who earns $54,000, the second response provides the most accurate interpretation of the piecewise linear function regarding how their income will be taxed:
"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 response correctly breaks down the income into segments according to the tax brackets. Here's how it works out:
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10% on the first $9,275: This means the first $9,275 of income is taxed at this lower rate.
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15% on the next $28,375: This applies to the income from $9,276 to $37,650. The total in this bracket is $28,375 ($37,650 - $9,275).
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25% on the remaining amount: This applies to the income over $37,650. Since the client earns $54,000, the amount subject to this rate is $16,350 ($54,000 - $37,650).
This tiered tax structure is typical in progressive tax systems, where different portions of income are taxed at different rates.
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