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Equivalent quadratic expressions
Wage increase |
The salary of employees at a large firm is determined by their rank
and ranges from $1000 to $3000 a month. Preparing for
negotiations on a new employment contract, the employees have decided to reduce the
salary gaps within the company. To this end, they demanded that the monthly salary of
the employees now earning $1000 be doubled, while the salary
of those earning $3000 remain as is. For employees
whose salary is in between, they offered the following method to determine
their raise:
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| salary increase (in percentages) |
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current salary (in thousands of dollars) |
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Analyze the employees' proposal
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Construct a function describing:
- The dependence of employee salary after the raise on current salary.
- The dependence of the raise workers will receive on their current salary.
Display the graphs of these functions.
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Answer the following questions and display other correspondence rules for the two functions you created, which will emphasize the answers to these questions:
- What will be the highest salary according to the proposal? Who will receive it?
- What will be the lowest salary according to the proposal? Who will receive it?
- What will be the largest raise that an employee can receive? Who will get it?
- What will be the smallest raise that an employee can receive? Who will get it?
- Which employees will recieve a $3000 salary
(the largest salary before the increase) according to the propsal?
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Management objected to the proposal, claiming that according
to it there will be employees in the high ranks who will receive salaries that are lower than
those of some employees in the lower ranks. Make a different proposal, which the employees can adopt,
that eliminates the grounds for this objection. Present an analysis of your proposal. Is it better, as far as the employees are concerned, than the employees' original proposal? Does it
reduce the salary gaps in the company?
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