To determine the effective tax rate for a taxable income of \[tex]$95,600 using the provided piecewise function, follow these steps:
1. Identify the appropriate tax bracket:
Given that the taxable income is \$[/tex]95,600, it falls within the range \[tex]$89,076 to \$[/tex]170,050. According to the piecewise function, the corresponding formula to calculate the tax owed in this range is:
[tex]\[
f(x) = 0.24x - 6,104.50
\][/tex]
2. Calculate the tax owed:
Substitute \[tex]$95,600 as \( x \) in the formula:
\[
f(95,600) = 0.24 \cdot 95,600 - 6104.50
\]
Compute:
\[
0.24 \cdot 95,600 = 22,944
\]
Subtracting the constant:
\[
22,944 - 6,104.50 = 16,839.50
\]
Therefore, the tax owed for a taxable income of \$[/tex]95,600 is \[tex]$16,839.50.
3. Determine the effective tax rate:
The effective tax rate is defined as the percentage of the taxable income that is paid as taxes. It is calculated using the formula:
\[
\text{Effective Tax Rate} = \left(\frac{\text{Tax Owed}}{\text{Taxable Income}}\right) \times 100
\]
Substitute the values:
\[
\left(\frac{16,839.50}{95,600}\right) \times 100
\]
Compute the division:
\[
\frac{16,839.50}{95,600} \approx 0.1761
\]
Convert the result to a percentage:
\[
0.1761 \times 100 = 17.61\%
\]
4. Round the final answer to the nearest hundredth:
The calculated effective tax rate is 17.61%.
Thus, the effective tax rate for a taxable income of \$[/tex]95,600 is [tex]\(\boxed{17.61\%}\)[/tex].
