The table shows the number of weeks of vacation employees receive each year, based on the number of years they have been employed. What does [tex]$\forall(15)=5$[/tex] mean in terms of the problem?
| Years of Service | Weeks of Vacation |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 5 | 3 |
| 10 | 4 |
| 15 | 5 |
| 20 | 6 |
| 30 | 8 |
A. A worker took 5 weeks of vacation in 15 years.
B. A worker with 5 years of service gets 15 weeks of vacation each year.
C. There are 5 workers who have 15 years of service each.
D. A worker with 15 years of service gets 5 weeks of vacation each year.
Answer (2)
The expression ∀ ( 15 ) = 5 means that a worker with 15 years of service gets 5 weeks of vacation each year. Therefore, the correct answer is D.
Explanation
Understanding the Problem The problem provides a table that shows the relationship between an employee's years of service and the number of weeks of vacation they receive each year. The expression ∀ ( 15 ) = 5 represents a function where the input is 15 (years of service) and the output is 5 (weeks of vacation). We need to interpret this in the context of the problem and choose the correct option.
Interpreting the Expression The expression ∀ ( 15 ) = 5 means that when the years of service is 15, the weeks of vacation is 5. Looking at the table, we can see that a worker with 15 years of service gets 5 weeks of vacation each year.
Analyzing the Options Now, let's examine the given options:
A. A worker took 5 weeks of vacation in 15 years. - This is not the correct interpretation.
B. A worker with 5 years of service gets 15 weeks of vacation each year. - This is the opposite of what the expression means.
C. There are 5 workers who have 15 years of service each. - This is not related to the expression.
D. A worker with 15 years of service gets 5 weeks of vacation each year. - This matches our interpretation.
Final Answer Therefore, the correct answer is D. A worker with 15 years of service gets 5 weeks of vacation each year.
Examples
Understanding the relationship between years of service and vacation time is crucial in human resources. For instance, if a company wants to estimate the total vacation time employees will take in a year, they can use this table to predict vacation time based on employee tenure. This helps in planning workload distribution and ensuring adequate staffing levels throughout the year. This kind of analysis ensures that employees are rewarded for their loyalty and service, while the company can effectively manage its resources and operations.
The expression ∀ ( 15 ) = 5 indicates that a worker with 15 years of service is entitled to 5 weeks of vacation annually. Among the provided options, the correct interpretation is D. This shows how vacation time is tied to the length of employment in the company.
;
