Question

1. (3 points total) an employee must pay medicare tax at a base rate plus additional medicare tax if wages exceed a certain threshold. for a single person in 2022, the employees medicare tax in dollars was determined by the piecewise linear function below, where x is the employees medicare wages in thousands of dollars. (data from: internal revenue service.) you can use desmos to help you or you can do the math by hand, either way, the answer needs to be exact and not estimated.

$$ f ( x ) = \\left\\{ \
LATEXBLOCK0
\ ight. $$

(1 point each) find the function values
a. $$ f ( 0 ) = $$
b. $$ f ( 200 ) = $$
c. $$ f ( 400 ) = $$

Explanation:

Step1: Find \( f(0) \)

Since \( 0\leq0\leq200 \), use \( f(x) = 14.5x \).
Substitute \( x = 0 \) into \( f(x)=14.5x \):
\( f(0)=14.5\times0 \)
\( f(0) = 0 \)

Step2: Find \( f(200) \)

Since \( 0\leq200\leq200 \), use \( f(x)=14.5x \).
Substitute \( x = 200 \) into \( f(x)=14.5x \):
\( f(200)=14.5\times200 \)
\( f(200)=2900 \)

Step3: Find \( f(400) \)

Since \( 400>200 \), use \( f(x)=2900 + 23.5(x - 200) \).
Substitute \( x = 400 \) into \( f(x)=2900+23.5(x - 200) \):
First, calculate \( x - 200=400 - 200=200 \)
Then \( f(400)=2900+23.5\times200 \)
\( f(400)=2900 + 4700 \)
\( f(400)=7600 \)

Answer:

a. \( f(0)=0 \)
b. \( f(200)=2900 \)
c. \( f(400)=7600 \)