I need help with a question on functions and inequalities.

Question

 

1. Search results for "Given the function T(x) is the function used to calculate the annual tax liability of an individual in the country of Bonanza. Explain fully what you understand the function to be saying in terms of the taxation scale."

  T(x) =     0.05x                                        x < 90,000

                0.15(x - 90,000) + 4,500            90,000 < x < 140,000   

               0.25(x - 140,000) + 12,000        140,000 < x < 220,000

               0.35 ( x -220,000) + 32,000       x > 220,000

Answer 1

For earnings less than 90,000 per annum, the tax is 5% on those earnings. This makes the maximum tax 4,500.

Over 90,000 and up to 140,000, the tax rate increases to 15% on the earnings above 90,000 plus the maximum of 4,500 on the first 90,000. The maximum is 0.15*50,000 (140,000-90,000=50,000)=7,500+4,500=12,000.

Over 140,000 and up to 220,000, the tax increases to 25% on earnings above 140,000 plus the tax accumulated at the lower rates, 12,000. The maximum is 0.35*80,000=28,000 (220,000-140,000=80,000) plus 12,000=40,000.

Over 220,000, the tax is 35% on earnings above 220,000 plus 32,000, rather than the 40,000 accumulated at lower rates. There is no maximum upper limit.