Final answer:
The value of k is 20.
Step-by-step explanation:
To find the value of k, we need to work backwards from the given information. We know that in 2014, there were 540 kindergarten students enrolled. We also know that the number of students tripled each year until 2014. So, we can divide 540 by 3 to find the number of students in the previous year, which would be 180. Continuing this pattern, we divide 180 by 3 to find the number of students in the year before that, which would be 60. Finally, we divide 60 by 3 to find the number of students at the beginning of the 2011 school year, which is 20. Therefore, the value of k is 20.