Math Problem Statement
In a certain country, income tax is assessed using a piecewise function: f(x) = 0% if x ≤ 15,000, 12% if 15,000 < x ≤ 30,000, and 18% if x > 30,000. Determine the tax rate for incomes of $28,000 and $14,500.
Solution
To answer the questions based on the given piecewise function for income tax , let's break it down:
The function is defined as follows:
\begin{cases} 0\% & \text{if } x \leq 15,000 \\ 12\% & \text{if } 15,000 < x \leq 30,000 \\ 18\% & \text{if } x > 30,000 \end{cases}$$ ### a. If your income is $28,000, what percent of tax will you pay? Here, $$x = 28,000$$, which falls in the range $$15,000 < x \leq 30,000$$. According to the function, the tax rate is $$12\%$$. **Answer: You will pay 12% tax.** --- ### b. If your income is $14,500, what percent of tax will you pay? Here, $$x = 14,500$$, which falls in the range $$x \leq 15,000$$. According to the function, the tax rate is $$0\%$$. **Answer: You will pay 0% tax.** --- Would you like further clarification or additional details? ### Related Questions: 1. How much tax would you pay in dollars for an income of $28,000? 2. What is the tax for an income of $35,000 using this function? 3. What happens to the tax rate for incomes just above $15,000? 4. How would you rewrite this function if all ranges were expressed in terms of inequalities starting at 0? 5. What is the difference in tax rates between an income of $14,500 and $15,500? **Tip:** Understanding piecewise functions helps break down complex real-world rules like tax brackets into manageable parts.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise functions
Tax brackets
Algebra
Formulas
f(x) = {0%, 12%, 18% based on income ranges}
Theorems
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Suitable Grade Level
Grades 9-12