Please help me figure out this problem.

Mathematics
Tutor: None Selected Time limit: 1 Day

The income tax T owed in a certain state is a function of the taxable income I, both measured in dollars. The formula is given below.
T = 0.14I − 100
(a) Express using functional notation the tax owed on a taxable income of $12,000.
T 

Calculate the tax owed on a taxable income of $12,000.
 
 

(b) If your taxable income increases from $12,000 to $14,000, by how much does your tax increase?
 

(c) If your taxable income increases from $14,000 to $16,000, by how much does your tax increase?
 
Aug 28th, 2015

Hi there! Thank you for the opportunity to help you with your question!

(a) The income I = 12000 in this case, so the functional form is T(12000)

 the tax owed on an income of 12,000 is given by T(12000) = 0.14*12,000-100 = 1580

(b) At 14,000, your tax is T(14,000) = 0.14*14,000 -100 = 1860

The increase equals the tax at 14,000, minus the tax at 12,000 or 1860-1580 = 280

(c) At 16,000, your tax is T(16,000) = 0.14*16,000-100 = 2140

The increase equals the tax at 16,000, minus the tax at 14,000 or 2140 - 1860 = 280

Please let me know if you need any clarification. Always glad to help!
Aug 28th, 2015

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