QuestionCalculate the Medicare tax function values for $x = 0$ , $200$ , and $400$ using the piecewise function defined for 2022.

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is a piecewise linear function. The function $f(x)$ is defined as follows - $f(x) =16.5x$ if $0 \leq x \leq200$ - $f(x) =3300 +26.5(x -200)$ if $x >200$
3. We need to find the function values $f(0)$ , $f(200)$ , and $f(400)$

STEP 2

First, let's find the function value $f(0)$ . According to the function definition, we use the first equation $f(x) =16.5x$ for $0 \leq x \leq200$ . $f(0) =16.5 \times0$

STEP 3

Calculate the function value $f(0)$ .
$f(0) =16.5 \times0 =0$

STEP 4

Next, let's find the function value $f(200)$ . According to the function definition, we use the first equation $f(x) =16.x$ for $0 \leq x \leq200$ .
$f(200) =16. \times200$

STEP 5

Calculate the function value $f(200)$ .
$f(200) =16.5 \times200 =3300$

STEP 6

Finally, let's find the function value $f(400)$ . According to the function definition, we use the second equation $f(x) =3300 +26.5(x -200)$ for $x >200$ .
$f(400) =3300 +26.5 \times (400 -200)$

STEP 7

Calculate the function value $f(400)$ .
$f(400) =3300 +26.5 \times (400 -200) =3300 +26.5 \times200 =8600$ So, the function values are $f(0) =0$ , $f(200) =3300$ , and $f(400) =8600$ .

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QuestionCalculate the Medicare tax function values for $x = 0$ , $200$ , and $400$ using the piecewise function defined for 2022.

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is a piecewise linear function. The function $f(x)$ is defined as follows - $f(x) =16.5x$ if $0 \leq x \leq200$ - $f(x) =3300 +26.5(x -200)$ if $x >200$
3. We need to find the function values $f(0)$ , $f(200)$ , and $f(400)$

STEP 2

First, let's find the function value $f(0)$ . According to the function definition, we use the first equation $f(x) =16.5x$ for $0 \leq x \leq200$ . $f(0) =16.5 \times0$

STEP 3

Calculate the function value $f(0)$ .
$f(0) =16.5 \times0 =0$

STEP 4

Next, let's find the function value $f(200)$ . According to the function definition, we use the first equation $f(x) =16.x$ for $0 \leq x \leq200$ .
$f(200) =16. \times200$

STEP 5

Calculate the function value $f(200)$ .
$f(200) =16.5 \times200 =3300$

STEP 6

Finally, let's find the function value $f(400)$ . According to the function definition, we use the second equation $f(x) =3300 +26.5(x -200)$ for $x >200$ .
$f(400) =3300 +26.5 \times (400 -200)$

STEP 7

Calculate the function value $f(400)$ .
$f(400) =3300 +26.5 \times (400 -200) =3300 +26.5 \times200 =8600$ So, the function values are $f(0) =0$ , $f(200) =3300$ , and $f(400) =8600$ .

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QuestionCalculate the Medicare tax function values for x=0x = 0x=0, 200200200, and 400400400 using the piecewise function defined for 2022.

Studdy Solution

STEP 1

STEP 2

First, let's find the function value f(0)f(0)f(0). According to the function definition, we use the first equation f(x)=16.5xf(x) =16.5xf(x)=16.5x for 0≤x≤2000 \leq x \leq2000≤x≤200.f(0)=16.5×0f(0) =16.5 \times0f(0)=16.5×0

STEP 3

Calculate the function value f(0)f(0)f(0).f(0)=16.5×0=0f(0) =16.5 \times0 =0f(0)=16.5×0=0

STEP 4

Next, let's find the function value f(200)f(200)f(200). According to the function definition, we use the first equation f(x)=16.xf(x) =16.xf(x)=16.x for 0≤x≤2000 \leq x \leq2000≤x≤200.f(200)=16.×200f(200) =16. \times200f(200)=16.×200

STEP 5

Calculate the function value f(200)f(200)f(200).f(200)=16.5×200=3300f(200) =16.5 \times200 =3300f(200)=16.5×200=3300

STEP 6

STEP 7

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QuestionCalculate the Medicare tax function values for $x = 0$ , $200$ , and $400$ using the piecewise function defined for 2022.

First, let's find the function value $f(0)$ . According to the function definition, we use the first equation $f(x) =16.5x$ for $0 \leq x \leq200$ . $f(0) =16.5 \times0$

Calculate the function value $f(0)$ .
$f(0) =16.5 \times0 =0$

Next, let's find the function value $f(200)$ . According to the function definition, we use the first equation $f(x) =16.x$ for $0 \leq x \leq200$ .
$f(200) =16. \times200$

Calculate the function value $f(200)$ .
$f(200) =16.5 \times200 =3300$