Chapter 2.4, Problem 52E

Income tax In a given year, the U.S. federal income tax owed by a married couple filing jointly can be found from the following table (Source: internal Revenue Service, From $1040$

Instruction). $\begin{array}{l}\\ \begin{array}{l}\text{Married Filling jointly}\hfill \\ \begin{array}{ll}\text{Taxable income}\hfill & \text{ Tax Rate }\hfill \\ \text{\$0-\$18,550}\hfill & \text{10\%}\hfill \\ \text{\$18,551-\$75,300}\hfill & \text{\$1,855 plus 15\% of the amount over \$18,550}\hfill \\ \text{\$75,301-\$151,900}\hfill & \text{\$10,367}\text{.50 plus 28\% of the amount over \$75,300}\hfill \\ \text{\$151,901-\$231,450}\hfill & \text{\$29,517}\text{.50 plus 28\% of the amount over \$151,900}\hfill \\ \text{\$231,451-\$413,350}\hfill & \text{\$151,791}\text{.50 plus 33\% of the amount over \$231,450}\hfill \\ \text{\$413,351-\$466,950}\hfill & \text{\$111,818}\text{.50 plus 35\% of the amount over \$413,450}\hfill \\ \text{\$466,951ormore}\hfill & \text{\$130,578}\text{.50 plus39}\text{.6\% of the amount over \$466,950}\hfill \end{array}\hfill \end{array}\end{array}$

For incomes up to $\$151,900$, write the pricewise defined function $T$ with input $x$ that models the federal tax dollars due as a function of $x$, the taxable income dollars earned.

Use the function to find $T(70,000)$.

Find the tax due on a taxable income of $\$100,000$.

A friend tells Jack Waddell not to earn any money over $\$75,300$ because it will raise his tax rate to $25\%$ on all of his taxable income. Test this statement by finding the tax due on $\$75,300$ and $\$75,300+\$1$. What do you conclude?