QuestionAn employee's Medicare tax is given by a piecewise function. Find $f(0)$ , $f(200)$ , and $f(400)$ for $f(x)$ .
$f(x)=\left\{\begin{array}{ll} 13.5 x & \text { if } 0 \leq x \leq 200 \\ 2700+26.5(x-200) & \text { if } x>200 \end{array}\right.$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is a piecewise linear function that describes the employee's Medicare tax in dollars. . $x$ is the employee's Medicare wages in thousands of dollars.
3. The function is defined as $f(x) =13.5x$ for $0 \leq x \leq200$ and $f(x) =2700+26.5(x-200)$ for $x >200$ .

STEP 2

First, we need to find the function value $f(0)$ . Since $0$ falls in the interval $0 \leq x \leq200$ , we use the function $f(x) =13.5x$ .
$f(0) =13.5 \times0$

STEP 3

Calculate the function value $f(0)$ .
$f(0) =13.5 \times0 =0$

STEP 4

Next, we need to find the function value $f(200)$ . Since $200$ falls in the interval $0 \leq x \leq200$ , we use the function $f(x) =13.x$ .
$f(200) =13. \times200$

STEP 5

Calculate the function value $f(200)$ .
$f(200) =13.5 \times200 =2700$

STEP 6

Finally, we need to find the function value $f(400)$ . Since $400$ is greater than $200$ , we use the function $f(x) =2700+26.5(x-200)$ .
$f(400) =2700 +26.5 \times (400 -200)$

STEP 7

Calculate the function value $f(400)$ .
$f(400) =2700 +26.5 \times (400 -200) =2700 +26.5 \times200 =2700 +5300 =8000$ So, the function values are $f(0) =0$ , $f(200) =2700$ , and $f(400) =8000$ .

Was this helpful?

QuestionAn employee's Medicare tax is given by a piecewise function. Find $f(0)$ , $f(200)$ , and $f(400)$ for $f(x)$ .
$f(x)=\left\{\begin{array}{ll} 13.5 x & \text { if } 0 \leq x \leq 200 \\ 2700+26.5(x-200) & \text { if } x>200 \end{array}\right.$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is a piecewise linear function that describes the employee's Medicare tax in dollars. . $x$ is the employee's Medicare wages in thousands of dollars.
3. The function is defined as $f(x) =13.5x$ for $0 \leq x \leq200$ and $f(x) =2700+26.5(x-200)$ for $x >200$ .

STEP 2

First, we need to find the function value $f(0)$ . Since $0$ falls in the interval $0 \leq x \leq200$ , we use the function $f(x) =13.5x$ .
$f(0) =13.5 \times0$

STEP 3

Calculate the function value $f(0)$ .
$f(0) =13.5 \times0 =0$

STEP 4

Next, we need to find the function value $f(200)$ . Since $200$ falls in the interval $0 \leq x \leq200$ , we use the function $f(x) =13.x$ .
$f(200) =13. \times200$

STEP 5

Calculate the function value $f(200)$ .
$f(200) =13.5 \times200 =2700$

STEP 6

Finally, we need to find the function value $f(400)$ . Since $400$ is greater than $200$ , we use the function $f(x) =2700+26.5(x-200)$ .
$f(400) =2700 +26.5 \times (400 -200)$

STEP 7

Calculate the function value $f(400)$ .
$f(400) =2700 +26.5 \times (400 -200) =2700 +26.5 \times200 =2700 +5300 =8000$ So, the function values are $f(0) =0$ , $f(200) =2700$ , and $f(400) =8000$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

First, we need to find the function value f(0)f(0)f(0). Since 000 falls in the interval 0≤x≤2000 \leq x \leq2000≤x≤200, we use the function f(x)=13.5xf(x) =13.5xf(x)=13.5x.f(0)=13.5×0f(0) =13.5 \times0f(0)=13.5×0

STEP 3

Calculate the function value f(0)f(0)f(0).f(0)=13.5×0=0f(0) =13.5 \times0 =0f(0)=13.5×0=0

STEP 4

Next, we need to find the function value f(200)f(200)f(200). Since 200200200 falls in the interval 0≤x≤2000 \leq x \leq2000≤x≤200, we use the function f(x)=13.xf(x) =13.xf(x)=13.x.f(200)=13.×200f(200) =13. \times200f(200)=13.×200

STEP 5

Calculate the function value f(200)f(200)f(200).f(200)=13.5×200=2700f(200) =13.5 \times200 =2700f(200)=13.5×200=2700

STEP 6

Finally, we need to find the function value f(400)f(400)f(400). Since 400400400 is greater than 200200200, we use the function f(x)=2700+26.5(x−200)f(x) =2700+26.5(x-200)f(x)=2700+26.5(x−200).f(400)=2700+26.5×(400−200)f(400) =2700 +26.5 \times (400 -200)f(400)=2700+26.5×(400−200)

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

First, we need to find the function value $f(0)$ . Since $0$ falls in the interval $0 \leq x \leq200$ , we use the function $f(x) =13.5x$ .
$f(0) =13.5 \times0$

Calculate the function value $f(0)$ .
$f(0) =13.5 \times0 =0$

Next, we need to find the function value $f(200)$ . Since $200$ falls in the interval $0 \leq x \leq200$ , we use the function $f(x) =13.x$ .
$f(200) =13. \times200$

Calculate the function value $f(200)$ .
$f(200) =13.5 \times200 =2700$

Finally, we need to find the function value $f(400)$ . Since $400$ is greater than $200$ , we use the function $f(x) =2700+26.5(x-200)$ .
$f(400) =2700 +26.5 \times (400 -200)$