Chapter 3.1, Problem 42AE

Competitive Balance Tax In 2011, major league baseball signed a labor agreement with the players. In this agreement, any team whose payroll exceeded $\$189$ million in 2015 had to pay a competitive balance tax of 50% (for four or more consecutive offenses). The linear function $T\left(p\right)=0.50\left(p-189\right)$ describes the competitive balance tax $T$ of a team whose payroll was $p$ (in millions of dollars).

Source: Major League Baseball

a. What is the implied domain of this linear function?

b. What was the competitive balance tax for the New York Yankees whose 2015 payroll was $\$214.2$ million?

c. Graph the linear function.

d. What was the payroll of a team that paid a competitive balance tax of $\$15.7$ million?

e. Interpret the slope.