QuestionCalculate the income tax $h(x)$ for a single person given the rules. Find $h(1260)$ , $h(7160)$ , and $h(49070)$ . Round $h(49070)$ to the nearest cent.

Studdy Solution

STEP 1

Assumptions1. The income tax function $h(x)$ is given by the piecewise function $h(x)=\left\{\begin{array}{ll} 0.02 x, & \text { if }0 \leq x<6000 \\ 120+0.03(x-6000), & \text { if }6000 \leq x<11,000 \\ 270+0.04(x-11,000), & \text { if } x \geq11,000\end{array}\right.$ . We are asked to find the values of $h(1260)$ , $h(7160)$ , and $h(49,070)$ .
3. The taxable income is a non-negative real number.

STEP 2

First, let's find the value of $h(1260)$ . Since $1260$ is between $0$ and $6000$ , we use the first rule of the piecewise function.
$h(1260) =0.02 \times1260$

STEP 3

Calculate the value of $h(1260)$ .
$h(1260) =0.02 \times1260 = \$25.20$

STEP 4

Now, let's find the value of $h(7160)$ . Since $7160$ is between $6000$ and $11000$ , we use the second rule of the piecewise function.
$h(7160) =120 +0.03 \times (7160 -6000)$

STEP 5

Calculate the value of $h(7160)$ .
$h(7160) =120 +0.03 \times (7160 -6000) =120 +0.03 \times1160 = \$174.80$

STEP 6

Finally, let's find the value of $h(49,070)$ . Since $49,070$ is greater than $11000$ , we use the third rule of the piecewise function.
$h(49,070) =270 +0.04 \times (49,070 -11,000)$

STEP 7

Calculate the value of $h(49,070)$ .
$h(49,070) =270 +0.04 \times (49,070 -11,000) =270 +0.04 \times38,070 = \$1,792.80$ Interpretation $h(1260)$ means that a single person with a taxable income of $1260$ will pay \ $25.20 in state income tax.$ h(7160) $means that a single person with a taxable income of$ 7160 $will pay \$174.80 in state income tax.$ h(49,070) $means that a single person with a taxable income of$ 49,070$ will pay \$1,792.80 in state income tax.

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QuestionCalculate the income tax $h(x)$ for a single person given the rules. Find $h(1260)$ , $h(7160)$ , and $h(49070)$ . Round $h(49070)$ to the nearest cent.

Studdy Solution

STEP 1

STEP 2

First, let's find the value of $h(1260)$ . Since $1260$ is between $0$ and $6000$ , we use the first rule of the piecewise function.
$h(1260) =0.02 \times1260$

STEP 3

Calculate the value of $h(1260)$ .
$h(1260) =0.02 \times1260 = \$25.20$

STEP 4

Now, let's find the value of $h(7160)$ . Since $7160$ is between $6000$ and $11000$ , we use the second rule of the piecewise function.
$h(7160) =120 +0.03 \times (7160 -6000)$

STEP 5

Calculate the value of $h(7160)$ .
$h(7160) =120 +0.03 \times (7160 -6000) =120 +0.03 \times1160 = \$174.80$

STEP 6

Finally, let's find the value of $h(49,070)$ . Since $49,070$ is greater than $11000$ , we use the third rule of the piecewise function.
$h(49,070) =270 +0.04 \times (49,070 -11,000)$

STEP 7

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QuestionCalculate the income tax h(x)h(x)h(x) for a single person given the rules. Find h(1260)h(1260)h(1260), h(7160)h(7160)h(7160), and h(49070)h(49070)h(49070). Round h(49070)h(49070)h(49070) to the nearest cent.

Studdy Solution

STEP 1

STEP 2

First, let's find the value of h(1260)h(1260)h(1260). Since 126012601260 is between 000 and 600060006000, we use the first rule of the piecewise function.h(1260)=0.02×1260h(1260) =0.02 \times1260h(1260)=0.02×1260

STEP 3

Calculate the value of h(1260)h(1260)h(1260).h(1260)=0.02×1260=$25.20h(1260) =0.02 \times1260 = \$25.20h(1260)=0.02×1260=$25.20

STEP 4

Now, let's find the value of h(7160)h(7160)h(7160). Since 716071607160 is between 600060006000 and 110001100011000, we use the second rule of the piecewise function.h(7160)=120+0.03×(7160−6000)h(7160) =120 +0.03 \times (7160 -6000)h(7160)=120+0.03×(7160−6000)

STEP 5

Calculate the value of h(7160)h(7160)h(7160).h(7160)=120+0.03×(7160−6000)=120+0.03×1160=$174.80h(7160) =120 +0.03 \times (7160 -6000) =120 +0.03 \times1160 = \$174.80h(7160)=120+0.03×(7160−6000)=120+0.03×1160=$174.80

STEP 6

Finally, let's find the value of h(49,070)h(49,070)h(49,070). Since 49,07049,07049,070 is greater than 110001100011000, we use the third rule of the piecewise function.h(49,070)=270+0.04×(49,070−11,000)h(49,070) =270 +0.04 \times (49,070 -11,000)h(49,070)=270+0.04×(49,070−11,000)

STEP 7

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QuestionCalculate the income tax $h(x)$ for a single person given the rules. Find $h(1260)$ , $h(7160)$ , and $h(49070)$ . Round $h(49070)$ to the nearest cent.

First, let's find the value of $h(1260)$ . Since $1260$ is between $0$ and $6000$ , we use the first rule of the piecewise function.
$h(1260) =0.02 \times1260$

Calculate the value of $h(1260)$ .
$h(1260) =0.02 \times1260 = \$25.20$

Now, let's find the value of $h(7160)$ . Since $7160$ is between $6000$ and $11000$ , we use the second rule of the piecewise function.
$h(7160) =120 +0.03 \times (7160 -6000)$

Calculate the value of $h(7160)$ .
$h(7160) =120 +0.03 \times (7160 -6000) =120 +0.03 \times1160 = \$174.80$

Finally, let's find the value of $h(49,070)$ . Since $49,070$ is greater than $11000$ , we use the third rule of the piecewise function.
$h(49,070) =270 +0.04 \times (49,070 -11,000)$