Question

3. The following table shows the federal income tax owed by a single taxpayer for the given level of taxable income for 2015. Both are measured in dollars.

Taxable Income 97000 97050 97100 97150 97200 97250 97300 Tax Owed 20238 20252 20266 20280 20294 20308 20372 a) Show that, over the range of taxable income shown in the table, the tax owed is a linear function of taxable income. b) What tax do you owe if you have a taxable income of 97150? c) How much additional tax is due on each dollar of taxable income over 97000? d) Let A denote the amount (dollars) of your taxable income in excess of $97000 and T the tax (in dollars) you owe. Find a linear formula that gives T in terms of A. (15)

Answer 1

a) Taxable income Tax owed (x) (y) Additional taxable income Additional tax owed Additional tax owed Additional taxable income 14 0.28 14 97,000 97,050 97,100 97,150 97,200 97,250 97,300 20,238 20,252 20,266 20,280 20,294 20,308 20,322 14 50 50 50 50 50 50 14 0.28 0.28 0.28 0.28 0.28 14 14 Slope = Additional taxable income = 0.28 = Constant Additional tax owed It can be seen from the above table that with every $50 increase in taxable income, the tax owed increases by $14. Therefore, it can be inferred that the tax owed is a linear function of taxable income. b) At taxable income of 97150, the tax owed is 20,280. c) Additional tax due on each dollar of taxable income over 97,000 is 0.28 d) y - 20,238 = slope(x - 97,000) Tax owed = 20,238 +0.28(Taxable income - 97,000) Therefore, T = 20,238 +0.28A Tax owed =T Taxable income - 97,000 = A