Answer:
Your answer choice is correct: the range 15,000–40,000
Step-by-step explanation:
Above income of 15,000 and below income of 40,000, the problem statement tells us the tax rate is 5%. If income amount is represented by x, then .05x is the amount of the tax (subject to the credits offered by the graduated scale). The term 0.05x in the question tells you the applicable range is 15,000 ≤ x ≤ 40,000.
If 15,000 were taxed at the 5% rate, the tax amount would be $750. Instead, the tax amount on that income is 3% of 15,000, or $450—a tax that is $300 less than 0.05x. Hence in the range 15,000–40,000, the tax computation is ...
... f(x) = 0.05x -300 . . . . . for 15,000 ≤ x ≤ 40,000
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<em>Above 40,000</em>
At the middle income tax rate, $40,000 would have a tax of ...
... 0.05×40000 -300 = 1700
At 7%, $40,000 would have a tax of
... 0.07×40000 = 2800
Then the actual tax on amounts above $40,000 is $1100 less than 7% of the income.
... f(x) = 0.07x -1100 . . . . . for x ≥ 40,000
