Let's interpret the notation [tex]\( K(15) = 5 \)[/tex].
In this context, [tex]\( K \)[/tex] is a function that represents the number of weeks of vacation employees receive based on their years of service. The value inside the parentheses, in this case, 15, indicates the number of years an employee has worked. The value of the function, 5, is the corresponding number of weeks of vacation.
Hence, [tex]\( K(15) = 5 \)[/tex] means that an employee who has been employed for 15 years receives 5 weeks of vacation each year.
Given this explanation, the correct interpretation among the provided options is:
C. A worker with 15 years of service gets 5 weeks of vacation each year.