To determine the effective tax rate for a taxable income of \[tex]$63,425 using the piecewise function given, we'll follow these detailed steps:
1. Identify the correct tax bracket:
For a taxable income of \$[/tex]63,425, we need to determine the appropriate tax bracket from the provided chart and piecewise function.
According to the chart, the taxable income \[tex]$63,425 falls into the third bracket:
\[
\$[/tex]41,176 - \[tex]$89,075 \quad \text{with a marginal tax rate of} \quad 22\%
\]
Correspondingly, for this bracket, the piecewise function is:
\[
f(x) = 0.22x - 4,323.00
\]
2. Calculate the amount of taxes owed:
Substitute \( x = 63,425 \) into the piecewise function:
\[
f(63,425) = 0.22 \times 63,425 - 4,323.00
\]
Carry out the multiplication first:
\[
0.22 \times 63,425 = 13,953.50
\]
Subtract 4,323.00 from the result:
\[
13,953.50 - 4,323.00 = 9,630.50
\]
So, the total amount of taxes owed is:
\[
f(63,425) = 9,630.50
\]
3. Calculate the effective tax rate:
The effective tax rate is given by the ratio of the tax owed to the taxable income, expressed as a percentage. Using the formula:
\[
\text{Effective Tax Rate} = \left( \frac{f(x)}{x} \right) \times 100
\]
Substitute \( f(x) = 9,630.50 \) and \( x = 63,425 \):
\[
\text{Effective Tax Rate} = \left( \frac{9,630.50}{63,425} \right) \times 100
\]
Perform the division:
\[
\frac{9,630.50}{63,425} \approx 0.1518
\]
Convert the decimal to a percentage:
\[
0.1518 \times 100 = 15.18\%
\]
4. Round the effective tax rate to the nearest hundredth:
The effective tax rate for a taxable income of \$[/tex]63,425 is [tex]\( 15.18\% \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{15.18\%}
\][/tex]
