Single Variable Calculus, Chapter 1, 1.1, Section 1.1, Problem 59

The following are the income tax assessed in a certain country.

- No tax for an income up to \$10,000

- If the income is more than \$10,000 up to \$20,000 the tax is rate at 10%

- If the income is more than \$20,000 the tax rate is 15%


(a) Sketch the graph of the tax rate $R$ as a function of income $I$








The graph shows the tax rate $R$ as function of the income $I$.



(b) How much tax is assessed on an income of \$14,000? On \$26,000?



Since \$14,000 is greater than \$10,000 its tax rate is 10%


Tax on \$14,000 = \$ $(14,000 - 10,000)(10\%)$


Tax on \$14,000 = \$ $(14,000 - 10,000)(0.10)$


Tax on \$14,000 = \$$14,000(0.10)$


Tax on \$14,000 = $\$400$


Since \$26,000 is greater than \$10,000 its tax rate is 15%



Tax on \$26,000 = \$ $(26,000 - 10,000)(15\%)$


Tax on \$26,000 = \$ $(26,000 - 10,000)(0.15)$


Tax on \$26,000 = \$$26,000(0.15)$


Tax on \$26,000 = $\$2,400$




(c) Sketch the graph of the total assessed tax $T$ as the function of income $I$.









The graph shows the total assessed tax $T$ as the function of income $I$.