In a particular state and for a particular​ year, the income tax rates for a single person were as follows. A 3​% tax of the first ​$8100 ​earned, 3.75​% of the next ​$3200 ​earned, 4.5​% of the next ​$2050 ​earned, 5.9​% of the next ​$7100 ​earned, 6.45​% of the next ​$56 comma 600 ​earned, 6.65​% of the next ​$128 comma 600 ​earned, 6.85​% of the next ​$823 comma 300 ​earned, and 8.86​% of any amount earned over ​$1 comma 028 comma 950. Let​ f(x) represent the amount of tax owed on an income of x dollars. Answer parts​ (a) through​ (f) below and in parts​ (a) through​ (d) explain in a sentence what the answer means.

give me theanswer for the first 4 parts

Part 1

​(a)​ f(50000​)equals
  
enter your response here

This means a tax of ​$
  
enter your response here was due on an income of ​$
  
enter your response here.

To find the amount of tax owed on an income of $50,000 using the provided tax rates, we will calculate the tax owed for each bracket and sum it up.

### Step-by-step breakdown of tax calculation:

1. **First bracket: 3% on the first $8,100**
   \[
   0.03 \times 8100 = 243
   \]
   Tax on the first $8,100 = $243.

2. **Second bracket: 3.75% on the next $3,200** 
   \[
   0.0375 \times 3200 = 120
   \]
   Tax on the next $3,200 = $120.

3. **Third bracket: 4.5% on the next $2,050**
   \[
   0.045 \times 2050 = 92.25
   \]
   Tax on the next $2,050 = $92.25.

4. **Fourth bracket: 5.9% on the next $7,100**
   \[
   0.059 \times 7100 = 419.90
   \]
   Tax on the next $7,100 = $419.90.

5. **Fifth bracket: 6.45% on the next $56,600, but only part of it applies since the income is $50,000, and the total amount taxed until now is $20,450. This leaves $50,000 - $20,450 = $29,550 taxable at 6.45%.**
   \[
   0.0645 \times 29,550 = 1905.48
   \]
   Tax on the remaining $29,550 = $1,905.48.

### Total tax owed:
\[
243 + 120 + 92.25 + 419.90 + 1905.48 = 2780.63
\]

### Part (a): $ f(50,000) $
\[
f(50,000) = 2780.63
\]
This means a tax of **$2,780.63** was due on an income of **$50,000**.

---

Would you like more details or explanations?

### Here are 5 related questions:
1. How would the tax change for an income of $60,000?
2. What is the tax rate on an income of $100,000?
3. How much tax would be owed on an income of $1,000,000?
4. What is the marginal tax rate for someone earning $50,000?
5. How would the tax be different for a married couple with the same income?

### Tip:
Always remember to apply each tax rate only to the portion of income within the corresponding bracket.

In a particular state and for a particular year, the income tax rates for a single person were as follows. A 3% tax of the first $8,100 earned, 3.75% of the next $3,200 earned, 4.5% of the next $2,050 earned, 5.9% of the next $7,100 earned, 6.45% of the next $56,600 earned, 6.65% of the next $128,600 earned, 6.85% of the next $823,300 earned, and 8.86% of any amount earned over $1,028,950. Let f(x) represent the amount of tax owed on an income of x dollars. Answer parts (a) through (f) below and in parts (a) through (d) explain in a sentence what the answer means.

(a) f(50000) =
This means a tax of
was due on an income of

Learn how to calculate the income tax owed on an income of $50,000 using a progressive tax system. This problem involves piecewise functions and arithmetic, showing how tax is calculated in each bracket with a step-by-step breakdown.

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