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(Federal Income Taxes and Piecewise Functions LC)

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

Marginal Tax Rate Chart

\begin{tabular}{|l|l|}
\hline
Tax Bracket & Marginal Tax Rate \\
\hline
\[tex]$0 - \$[/tex]10,275 & 10\% \\
\hline
\[tex]$10,276 - \$[/tex]41,175 & 12\% \\
\hline
\[tex]$41,176 - \$[/tex]89,075 & 22\% \\
\hline
\[tex]$89,076 - \$[/tex]170,050 & 24\% \\
\hline
\[tex]$170,051 - \$[/tex]215,950 & 32\% \\
\hline
\[tex]$215,951 - \$[/tex]539,900 & 35\% \\
\hline
\$539,901+ & 37\% \\
\hline
\end{tabular}

[tex]
f(x) = \left\{
\begin{array}{ll}
0.10x, & 0 \leq x \leq 10,275 \\
0.12x - 205.50, & 10,276 \leq x \leq 41,175 \\
0.22x - 4,323.00, & 41,176 \leq x \leq 89,075 \\
0.24x - 6,104.50, & 89,076 \leq x \leq 170,050 \\
0.32x - 19,708.50, & 170,051 \leq x \leq 215,950 \\
0.35x - 26,187.00, & 215,951 \leq x \leq 539,900 \\
0.37x - 36,985.00, & x \geq 539,901
\end{array}
\right.
[/tex]

Determine the amount of taxes owed on a taxable income of [tex]\$49,652[/tex].

A. \[tex]$4,735.38

B. \$[/tex]6,600.44

C. \[tex]$7,709.92

D. \$[/tex]10,293.44



Answer :

GinnyAnswer
Let's determine the amount of taxes owed on a taxable income of [tex]$49,652. We know the tax brackets and the piecewise function for the taxable income. Given the taxable income \( x = 49,652 \), we have to first identify the appropriate tax bracket: - $[/tex]0-\[tex]$ 10,275$[/tex]: 10%
- [tex]$10,276-\$[/tex] 41,175[tex]$: 12% - $[/tex]41,176-\[tex]$ 89,075$[/tex]: 22%
- [tex]$89,076-\$[/tex] 170,050[tex]$: 24% - $[/tex]170,051-\[tex]$ 215,950$[/tex]: 32%
- [tex]$215,951-\$[/tex] 539,900[tex]$: 35% - above $[/tex]539,901[tex]$: 37% Taxable income \( \$[/tex]49,652 \) falls within the bracket [tex]\( \$41,176 - \$89,075 \)[/tex].

According to the piecewise function for this bracket:

- [tex]\( f(x) = 0.22x - 4,323.00 \)[/tex]

Plugging in [tex]\( x = 49,652 \)[/tex]:

[tex]\[ f(49,652) = 0.22 \times 49,652 - 4,323.00 \][/tex]

The calculation can break down as:
[tex]\[ 0.22 \times 49,652 = 10,923.44 \][/tex]
[tex]\[ 10,923.44 - 4,323.00 = 6,600.44 \][/tex]

So, the amount of taxes owed on a taxable income of [tex]$49,652 is: \[ \boxed{6,600.44} \] Thus, the correct answer is \(\$[/tex]6,600.44\).

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