Question

Many income tax systems are calculated using a tiered method. Under certain tax law, the first $100 000 of earning are subject to a 35% tax, earnings greater than $100 000 and up to $500 000 are subjects to a 45% tax. Any earnings greater than $500 000 are taxed at 55%. Write a piecewise function that models this situation.

Answer 1

Here is the step by step explaination
Tax = 0.35 * Earnings (Earnings < $100,000)

Tax = 0.35 * $100,000 + 0.45 * (Earnings - $100,000) ($100,000 < Earnings < $500,000)

Tax = 0.35 * $100,000 + 0.45 * $400,000 + 0.55 * (Earnings - $500,000)

(Earnings > $500,000)