Questions: The piecewise function represents the amount of taxes owed, f(x), as a function of the taxable income, x. Use the marginal tax rate chart or the piecewise function to answer the question. Marginal Tax Rate Chart Tax Bracket Marginal Tax Rate 0-10,275 10% 10,276-41,175 12% 41,176-89,075 22% 89,076-170,050 24% 170,051-215,950 32% 215,951-539,900 35% >539,901 37% f(x) = 0.10x, for 0 ≤ x ≤ 10,275 0.12x-205.50, for 10,276 ≤ x ≤ 41,175 0.22x-4,323.00, for 41,176 ≤ x ≤ 89,075 0.24x-6,104.50, for 89,076 ≤ x ≤ 170,050 0.32x-19,708.50, for 170,051 ≤ x ≤ 215,950 0.35x-26,187.00, for 215,951 ≤ x ≤ 539,900 0.37x-36,985.00, for x ≥ 539,901 Determine the effective tax rate for a taxable income of 63,425. Round the final answer to the nearest hundredth. - 10% - 14.67% - 15.18% - 22%

The piecewise function represents the amount of taxes owed, f(x), as a function of the taxable income, x. Use the marginal tax rate chart or the piecewise function to answer the question.

Marginal Tax Rate Chart

Tax Bracket  Marginal Tax Rate
0-10,275  10%
10,276-41,175  12%
41,176-89,075  22%
89,076-170,050  24%
170,051-215,950  32%
215,951-539,900  35%
>539,901  37%

f(x) = 
0.10x, for 0 ≤ x ≤ 10,275
0.12x-205.50, for 10,276 ≤ x ≤ 41,175
0.22x-4,323.00, for 41,176 ≤ x ≤ 89,075
0.24x-6,104.50, for 89,076 ≤ x ≤ 170,050
0.32x-19,708.50, for 170,051 ≤ x ≤ 215,950
0.35x-26,187.00, for 215,951 ≤ x ≤ 539,900
0.37x-36,985.00, for x ≥ 539,901


Determine the effective tax rate for a taxable income of 63,425. Round the final answer to the nearest hundredth.
- 10%
- 14.67%
- 15.18%
- 22%
Transcript text: the piecewise function represents the amount of taxes owed, $f(x)$, as a function of the taxable income, $x$. Use the marginal tax rate chart or the piecewise function to answer the question. Marginal Tax Rate Chart \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Tax Bracket } & Marginal Tax Rate \\ \hline$\$ 0-\$ 10,275$ & $10 \%$ \\ \hline$\$ 10,276-\$ 41,175$ & $12 \%$ \\ \hline$\$ 41,176-\$ 89,075$ & $22 \%$ \\ \hline$\$ 89,076-\$ 170,050$ & $24 \%$ \\ \hline$\$ 170,051-\$ 215,950$ & $32 \%$ \\ \hline$\$ 215,951-\$ 539,900$ & $35 \%$ \\ \hline$>\$ 539,901$ & $37 \%$ \\ \hline \end{tabular} \[ f(x)=\left\{\begin{array}{ll} 0.10 x, & 0 \leq x \leq 10,275 \\ 0.12 x-205.50, & 10,276 \leq x \leq 41,175 \\ 0.22 x-4,323.00, & 41,176 \leq x \leq 89,075 \\ 0.24 x-6,104,50, & 89,076 \leq x \leq 170,050 \\ 0.32 x-19,708,50, & 170,051 \leq x \leq 215,950 \\ 0.35 x-26,187.00, & 215,951 \leq x \leq 539,900 \\ 0.37 x-36,985,00, & x \geq 539,901 \end{array}\right. \] Determine the effective tax rate for a taxable income of $\$ 63,425$. Round the final answer to the nearest hundredth. $10 \%$ $14.67 \%$ $15.18 \%$ $22 \%$ Provious Ouestion Question 1 (Not Answered) 0 Next Question
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Solution

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Solution Steps

Step 1: Identify the Tax Bracket

The taxable income of \$63,425 falls within the range of \$41,176 to \$89,075. According to the marginal tax rate chart, this corresponds to the third tax bracket with a marginal tax rate of 22%.

Step 2: Calculate the Tax Owed

Using the piecewise function for the third tax bracket: \[ f(x) = 0.22x - 4,323.00 \] Substitute \(x = 63,425\): \[ f(63,425) = 0.22 \times 63,425 - 4,323.00 \] \[ f(63,425) = 13,953.50 - 4,323.00 \] \[ f(63,425) = 9,630.50 \]

Step 3: Calculate the Effective Tax Rate

The effective tax rate is calculated as: \[ \text{Effective Tax Rate} = \left(\frac{\text{Tax Owed}}{\text{Taxable Income}}\right) \times 100\% \] Substitute the values: \[ \text{Effective Tax Rate} = \left(\frac{9,630.50}{63,425}\right) \times 100\% \] \[ \text{Effective Tax Rate} = 0.1518 \times 100\% \] \[ \text{Effective Tax Rate} = 15.18\% \]

Final Answer

The effective tax rate for a taxable income of \$63,425 is \(\boxed{15.18\%}\).

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