Concept explainers
Competitive Balance Tax In 2011, major league baseball signed a labor agreement with the players. In this agreement, any team whose payroll exceeded million in 2015 had to pay a competitive balance tax of 50% (for four or more consecutive offenses). The linear function describes the competitive balance tax of a team whose payroll was (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 million?
c. Graph the linear function.
d. What was the payroll of a team that paid a competitive balance tax of million?
e. Interpret the slope.
To calculate:
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 million?
c. Graph the linear function.
d. What was the payroll of a team that paid a competitive balance tax of million?
e. Interpret the slope.
Answer to Problem 42AYU
Solution:
a. The domain of the given function is .
b. If the payroll is million, then the player has to pay a competitive balance tax of million.
c. The graph is shown below:
d. The payroll will be million.
e. If the payroll is increasing then the tax bill also is increasing.
Explanation of Solution
Given:
The given competitive balance tax function is
Calculation:
a. We can see that the variable in the given linear function can have any value more than 189, therefore, the domain of the given function is .
b. When , we have
Therefore, if the payroll is million, then the player has to pay a competitive balance tax of million.
c. The graph of the given linear function is
d. If , then we get
If the team paid a tax of million, then the payroll will be million.
e. We can see that the slope of the given function is which is a positive and is therefore increasing.
Thus, if the payroll is increasing then the tax bill also is increasing.
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