Question

A certain country taxes the first $22,000 of an individual's income at a rate of 10%, and all income over $22,000 is taxed at 25%. Find a piecewise-defined function T that specifies the total tax on an income of x dollars. (Simplify your answer completely.)

Answer 1

Answer:

T = {$0.01a     if a ≤ $22000

      $(0.25a - 3300)    if a > $22000}

Step-by-step explanation:

A country taxes the first $22000 of an individual's income at 10%.

If the income of an individual is = $a.

Tax up-to $22000 will be

= a × $\frac{10}{100}$

= $0.01a

Above $22000 tax deducted will be

= (a - 22000)×$\frac{25}{100}$

= 0.25a - 5500

= $(0.25a - 5500)

Total tax 'T' = 0.25a - 5500 + 2200

T = $(0.25a - 3300)

Piece-wise function will be  

T = {$0.01a     if a ≤ $22000

      $(0.25a - 3300)    if a > $22000}