https://file.aiquickdraw.com/mathbot/file/1727196420766jthd9a0a.jpg

Let's break down the problem based on the tax formula given in the image.

The tax formula is:

\[
T(x) = \begin{cases} 
0 & 0 \leq x \leq 15,000 \\
0.1x - 1500 & 15,000 < x \leq 180,000 \\
0.13x - 6900 & x > 180,000 
\end{cases}
\]

### 1. Dakota's Income ($300,000)
Dakota's income is $300,000, which falls in the range $x > 180,000$. So, we use the third part of the tax formula:
\[
T(300,000) = 0.13 \times 300,000 - 6900
\]
Let's compute it:
\[
T(300,000) = 39,000 - 6,900 = 32,100
\]
Dakota will pay **$32,100** in taxes.

### 2. Aliyah's Income ($10,000)
Aliyah's income is $10,000, which falls in the range $0 \leq x \leq 15,000$. According to the first part of the tax formula:
\[
T(10,000) = 0
\]
Aliyah will pay **$0** in taxes.

### 3. Enrique's Income ($70,000)
Enrique's income is $70,000, which falls in the range $15,000 < x \leq 180,000$. So, we use the second part of the tax formula:
\[
T(70,000) = 0.1 \times 70,000 - 1,500
\]
Let's compute it:
\[
T(70,000) = 7,000 - 1,500 = 5,500
\]
Enrique will pay **$5,500** in taxes.

### 4. New Tax Proposal for Enrique
The proposal suggests increasing the tax rate for incomes above $330,000 to 19%. However, Enrique's income is below $330,000, so **Enrique will not pay any additional taxes** under this proposal.

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Would you like to go into more detail or have any further questions?

Here are some related questions:
1. How does a progressive tax system like this one benefit lower-income earners?
2. What would happen if Dakota's income were $180,000 exactly?
3. How would Enrique's tax change if his income increased to $200,000?
4. If Aliyah earned $16,000, how much tax would she pay?
5. What is the average tax rate Dakota pays on her income?

**Tip**: Understanding tax brackets can help you calculate taxes for different income ranges more efficiently!

In a certain country, the amount of income tax T on earnings of x dollars is computed according to the formula:
T(x) = 0 for 0 ≤ x ≤ 15,000
T(x) = 0.1x - 1500 for 15,000 < x ≤ 180,000
T(x) = 0.13x - 6900 for x > 180,000.
Dakota has an income of $300,000. How much will they pay in taxes?
Aliyah has an income of $10,000. How much will they pay in taxes?
Enrique has an income of $70,000. How much will they pay in taxes?
A politician proposes increasing the tax rate, but only on those making more than $330,000, to 19%. How much more will Enrique pay in taxes?

Solve tax-related problems using piecewise functions to calculate how much Dakota, Aliyah, and Enrique pay in taxes based on their income levels. Learn how to apply different tax brackets and piecewise linear functions to compute tax for incomes above and below $180,000.

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