QuestionCalculate the tax $h(x)$ for incomes $x=1260$ , $x=7160$ , and $x=49070$ based on the given tax rules.

Studdy Solution

STEP 1

Assumptions1. The income tax is calculated according to the given piecewise function $h(x)$ . . The taxable income is represented by $x$ .
3. The function $h(x)$ is defined as follows - $h(x) =0.02x$ if $0 \leq x <6000$ - $h(x) =120 +0.03(x -6000)$ if $6000 \leq x <11000$ - $h(x) =270 +0.04(x -11000)$ if $x \geq11000$

STEP 2

To find the tax for a taxable income of $1260, we need to use the first part of the piecewise function because$ 1260 $is between$ 0 $and$ 6000$.
$h(1260) =0.02 \times1260$

STEP 3

Calculate the tax for a taxable income of $1260$ .
$h(1260) =0.02 \times1260 = \$25.20$

STEP 4

To find the tax for a taxable income of $7160, we need to use the second part of the piecewise function because$ 7160 $is between$ 6000 $and$ 11000$.
$h(7160) =120 +0.03 \times (7160 -6000)$

STEP 5

Calculate the tax for a taxable income of $7160$ .
$h(7160) =120 +0.03 \times (7160 -6000) = \$154.80$

STEP 6

To find the tax for a taxable income of $49070, we need to use the third part of the piecewise function because$ 49070 $is greater than$ 11000$.
$h(49070) =270 +0.04 \times (49070 -11000)$

STEP 7

Calculate the tax for a taxable income of $49070$ .
$h(49070) =270 +0.04 \times (49070 -11000) = \$181.80$ InterpretationsA. An individual with a taxable income of $1260$ will have to pay $25.20$ as tax. B. An individual with a taxable income of $7160$ will have to pay $154.80$ as tax. C. An individual with a taxable income of $49070$ will have to pay $181.80$ as tax.

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