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 ​$8200 ​earned, 3.5​% of the next ​$3200 ​earned, 4​% of the next ​$2150 ​earned, 5.9​% of the next ​$7200 ​earned, 6.45​% of the next ​$56 comma 400 ​earned, 6.65​% of the next ​$128 comma 800 ​earned, 6.85​% of the next ​$823 comma 100 ​earned, and 8.89​% of any amount earned over ​$1 comma 029 comma 050. 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. f(12 comma 000​)equals
  
enter your response here
This means a tax of ​$
  
enter your response here was due on an income of ​$
  
enter your response here.
​(Type integers or decimals rounded to the nearest hundredth as needed. Do not include the​ $ symbol in your​ answers.)

We are given different tax rates for various income brackets, and we are asked to calculate the amount of tax owed for an income of $12,000. Here's how to break it down based on the given income tax structure:

1. **For the first $8,200**:  
   - Tax rate: 3%  
   - Tax: $ 8,200 \times 0.03 = 246 $  
   
2. **For the next $3,200** (i.e., $8,200 to $11,400):  
   - Tax rate: 3.5%  
   - Tax: $ 3,200 \times 0.035 = 112 $  
   
3. **For the next $600** (since the income is $12,000, which is $600 more than $11,400):  
   - Tax rate: 4%  
   - Tax: $ 600 \times 0.04 = 24 $

### Total tax owed:
Now, let's sum up the taxes from each bracket:  
$ 246 + 112 + 24 = 382 $

### Final Answer:

- **f(12,000) = 382**
- This means a tax of **$382** was due on an income of **$12,000**.

Let me know if you would like further details or clarification! Here are some related questions:

1. How would the tax change if the income was $15,000?
2. What happens when income exceeds the highest tax bracket?
3. Can we model this tax system as a piecewise function?
4. How does the marginal tax rate affect the total tax paid as income increases?
5. How would tax deductions impact the calculation for someone earning $12,000?

**Tip**: When calculating taxes in multiple brackets, be sure to separate the portions of income that fall into each specific 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 $8200 earned, 3.5% of the next $3200 earned, 4% of the next $2150 earned, 5.9% of the next $7200 earned, 6.45% of the next $56,400 earned, 6.65% of the next $128,800 earned, 6.85% of the next $823,100 earned, and 8.89% of any amount earned over $1,029,050. 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. f(12,000) equals...

Learn how to calculate income tax for $12,000 using a marginal tax rate system. This problem explains the step-by-step breakdown of tax rates across income brackets, involving percentages, piecewise functions, and tax brackets. Suitable for high school students in Grades 10-12.

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