1. Recall our simplified version of the US Income tax system is given by the following: (i) Pay nothing on the first $12,000 you make; (ii) Pay 15% on any income beyond the first $12,000, up to $40,000; (iii) Pay 20% on any income beyond the first $40,000; up to $100,000; (iv) Then pay 35% of any income you made beyond the first $100,000; (a) If T (x), the tax function in dollars, on x dollars earned, then once again graph and write the piecewise linear function T (x). (b) So use your T (x) to write the function piecewise formula for P(x), the percentage tax due on income x. (c)For the income levels $22,000, $50,000, $120,000, and $1,000,000, find P (x). (d) Summarize the results from (c) in a well-labeled chart. (e)Calculate the limit too P (x). (f)Then in a couple of sentences, explain what (e) means. (g)Now suppose a million dollar earner successfully hides half of his income by incorporating in Delaware (or stashing it in the Cayman Islands). So how much income does he pay taxes on? [Complete sentence answer!!] Now find his effective tax percentage. (h) Find the amount an honest tax filer would have to earn in order to have the same tax percentage as (g). 1. Recall our simplified version of the US Income tax system is given by the following: (i) Pay nothing on the first $12,000 you make; (ii) Pay 15% on any income beyond the first $12,000, up to $40,000; (iii) Pay 20% on any income beyond the first $40,000; up to $100,000; (iv) Then pay 35% of any income you made beyond the first $100,000; (a) If T (x), the tax function in dollars, on x dollars earned, then once again graph and write the piecewise linear function T (x). (b) So use your T (x) to write the function piecewise formula for P(x), the percentage tax due on income x. (c)For the income levels $22,000, $50,000, $120,000, and $1,000,000, find P (x). (d) Summarize the results from (c) in a well-labeled chart. (e)Calculate the limit too P (x). (f)Then in a couple of sentences, explain what (e) means. (g)Now suppose a million dollar earner successfully hides half of his income by incorporating in Delaware (or stashing it in the Cayman Islands). So how much income does he pay taxes on? [Complete sentence answer!!] Now find his effective tax percentage. (h) Find the amount an honest tax filer would have to earn in order to have the same tax percentage as (g)