https://file.aiquickdraw.com/mathbot/file/1726596098529qjp1lq8o.jpg

Let's break down the problem step by step.

### a) Calculate the tax on $125,000:
- The first $50,000 is taxed at 5%.
- The remaining income above $50,000 is taxed at 12%.

1. For the first $50,000:
   \[
   \text{Tax on } 50,000 = 50,000 \times 0.05 = 2,500
   \]

2. For the income above $50,000, which is $125,000 - $50,000 = $75,000:
   \[
   \text{Tax on } 75,000 = 75,000 \times 0.12 = 9,000
   \]

3. Total tax:
   \[
   \text{Total tax} = 2,500 + 9,000 = 11,500
   \]

Thus, the total tax on $125,000 is **$11,500**.

### b) Write a function that models the tax policy:
Let $ T(x) $ be the tax on an income $ x $.

- If $ x \leq 50,000 $, the tax is 5% of $ x $:
  \[
  T(x) = 0.05x \quad \text{for} \quad 0 \leq x \leq 50,000
  \]

- If $ x > 50,000 $, the tax is 5% on the first $50,000 and 12% on the amount exceeding $50,000:
  \[
  T(x) = 0.05 \times 50,000 + 0.12 \times (x - 50,000) = 2,500 + 0.12 \times (x - 50,000) \quad \text{for} \quad x > 50,000
  \]

So the tax function $ T(x) $ is:
\[
T(x) =
\begin{cases}
0.05x & \text{if } 0 \leq x \leq 50,000 \\
2,500 + 0.12(x - 50,000) & \text{if } x > 50,000
\end{cases}
\]

Would you like further explanation or details on any part?

### Related questions:
1. How would the tax change if the second tax bracket was 15% instead of 12%?
2. What would the total tax be for an income of $200,000 using this tax policy?
3. Can you express this tax function as a single piecewise linear function?
4. How does the marginal tax rate affect higher-income earners in this model?
5. How would the total tax be impacted if the tax-free threshold increased to $60,000?

**Tip:** For piecewise functions, always carefully identify where the function switches from one rule to another based on given conditions.

A certain tax policy states that the first $50,000 of income is taxed at 5% and any income above $50,000 is taxed at 12%. a) Calculate the tax on $125,000. b) Write a function that models the tax policy.

Learn how to calculate the tax on $125,000 using a two-tier tax policy where income is taxed at 5% for the first $50,000 and 12% on the remaining income. Includes step-by-step calculations and a function that models the tax policy. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation