To determine the effective tax rate for a taxable income of [tex]$63,425, we need to follow a structured approach using the given piecewise function and tax brackets.
1. Identify which tax bracket the income falls into:
- The income of $[/tex]63,425 falls into the third bracket: [tex]\( \$41,176 \leq x \leq \$89,075 \)[/tex], which means the tax rate is [tex]\( 22\% \)[/tex].
2. Apply the corresponding piecewise function:
- For income in the range of [tex]\( \$41,176 \)[/tex] to [tex]\( \$89,075 \)[/tex], the tax owed can be calculated using the formula:
[tex]\[
f(x) = 0.22x - 4,323.00
\][/tex]
3. Calculate the tax owed:
- Substitute [tex]\( x = \$63,425 \)[/tex] into the piecewise function:
[tex]\[
f(63,425) = 0.22 \times 63,425 - 4,323.00
\][/tex]
4. Compute the tax value:
[tex]\[
f(63,425) = 0.22 \times 63,425 = 13,953.50
\][/tex]
[tex]\[
f(63,425) - 4,323.00 = 13,953.50 - 4,323.00 = 9,630.50
\][/tex]
So, the tax owed for an income of [tex]$63,425 is $[/tex]9,630.50.
5. Determine the effective tax rate:
- The effective tax rate is calculated by dividing the total tax by the total income and then multiplying by 100 to get a percentage:
[tex]\[
\text{Effective Tax Rate} = \left( \frac{\text{Tax}}{\text{Income}} \right) \times 100
\][/tex]
- Substitute the values into the formula:
[tex]\[
\text{Effective Tax Rate} = \left( \frac{9,630.50}{63,425} \right) \times 100
\][/tex]
6. Compute the effective tax rate:
- Perform the division:
[tex]\[
\frac{9,630.50}{63,425} \approx 0.1518
\][/tex]
- Convert to a percentage:
[tex]\[
0.1518 \times 100 = 15.18\%
\][/tex]
Therefore, the effective tax rate for a taxable income of $63,425 is [tex]\( 15.18\% \)[/tex].
The correct answer is [tex]\( 15.18\% \)[/tex].
