Income tax in a particular country is calculated according t

Income tax in a particular country is calculated according to the following rate schedule: 20% on the first $18,000 of income; 38% on the next $36,000 of income; 49% on any further income a. How much income tax should be paid by someone making $31,300? b. How much income tax should be paid by someone making $71,900? c. Construct a piecewise function that gives the tax for $x of income.

Solution

Let $x be the income and y be the income tax function

y = x*0.2 ; x <= 18000

= (x -18000)*0.38 ; 18000<x <= 54000

= ( x - 54000)*0.49 ; x> 54000

a) x = $31,300

y = 0.2*18000 + (31000 -18000)*0.38

= $8540

b) x = $ 71900

y = 0.2*18000 + 36000*0.38 + ( 71900 -18000 -36000)*0.49

= $ 26051