Answer:
- t is the amount of tax; i is the amount of income
- a) t = 0.05i
- b) t = 0.05i for i ≤ 100,000; t = 0.08i -3000 for i > 100,000
Explanation:
The steps are ...
- read and understand the problem statement
- do what it says
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We choose to define the variables t and i to represent the amount of tax and the amount of income, respectively. (Define your variables.)
The flat tax is simply 5% of income:
t = 5% × i
t = 0.05i . . . . . with the percentage expressed as a decimal (flat tax model)
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The graduated tax is the same as the flat tax for i ≤ 100,000. For income greater than 100,000, the excess income is taxed at a higher rate. (Income below that is still taxed at the flat tax rate.) The excess income is (i-100,000). So, a model for the graduated tax for incomes more than 100,000 is ...
t = .05 × 100,000 + 0.08 × (i -100,000) . . . . for i > 100,000
Terms can be combined so you have ...
t = 0.08i -3,000 . . . . for i > 100,000
Combining the flat tax portion of the function definition with the excess income portion of the function definition, you have the graduated tax model ...
t = 0.05i . . for i ≤ 100,000; t = 0.08i -3000 . . for i > 100,000