Chapter 3.2, Problem 1TU

TEST YOUR UNDERSTADING FOR EXAMPLE 3.3

The State of New York also has an income tax. The tax table for New York shows that a single New York resident with a taxable income of $\$15,000$ owes $\$671$ in New York income tax. If the taxable income is $\$15,500,$ then the table shows a tax liability of $\$701.$ Assume that the state tax is a linear function of taxable income, and find the tax owed if the taxable income is $\$15,350.$

EXAMPLE 3.3 OKLAHOMA INCOME TAX

The amount of income tax $T=T(l),$ in dollars, owed to the state of Oklahoma is a linear function of the taxable income $l,$ in dollars, at least over a suitably restricted range of incomes. According to the Oklahoma Income Tax table for the year $2015,$ a single Oklahoma resident taxpayer with a taxable income of $\$15,000$ owes $\$579$ in Oklahoma income tax. In functional notation, this is $T(15,000)=579.$ If the taxable income is $\$15,500,$ then the table shows a tax liability of $\$605.$

Part 1 Calculate the rate of change in $T$ with respect to $I,$ and explain in practical terms what it means.

Part 2 How much does the taxpayer owe if the taxable income is $\$15,350?$