Help with Precalc Question involving tax?

Question

Part of the Taxylvania tax rate table reads as follows:

A. If your taxable income is no more than $6,000, you owe 1% of your taxable income.

B. If your taxable income is more than $6,000 but no more than $18,000, you owe $60 plus 5% of the amount over $6,000.

C. If your taxable income is more than $18,000, you owe $660 plus 7% of the amount over $18,000.

If you were living in Taxylvania and your taxable income were $12,600, how much tax would you owe?

What if your taxable income were only $2,100?

We can give a formula for the tax T in terms of the income I if we give it in cases. For example, we have that T(I) = 0.01 I when I is less than $6,000. What formula gives the correct value for the tax when I is between $6,000 and $18,000?

T(I) =

Answer 1

1.  If your taxable income were $12.6K, you would owe:

(12,600 - 6000) * 5% + $60 = $390

2.  If your taxable income was $2,100 you would owe:

2,100 * 1% = $21

3.  When your taxable income is between $6K and $18K, the formula would look like:

T(I) = (I - 6000) * 5% + $60

Hope this helps.