Question

a states progressive math system can be modeled with the piecewise function:
\\( t(x) = \

$$\begin{cases} 0 & \\text{if } 0 \\leq x \\leq 20,000 \\\\ 0.12(x - 20,000) & \\text{if } 20,000 < x \\leq 50,000 \\\\ 3,600 + 0.17(x - 50,000) & \\text{if } x > 50,000 \\end{cases}$$

\\)
determine the amount of tax owed for a person with a taxable income of $55,000.
$\square

Explanation:

Step1: Identify applicable function piece

Since $x=55,000 > 50,000$, use $T(x)=3,600 + 0.17(x - 50,000)$.

Step2: Substitute $x=55,000$

$T(55,000)=3,600 + 0.17(55,000 - 50,000)$

Step3: Calculate the difference

$55,000 - 50,000 = 5,000$

Step4: Compute the tax portion

$0.17 \times 5,000 = 850$

Step5: Sum to get total tax

$3,600 + 850 = 4,450$

Answer:

$\$4,450$