activity = min(time * 14, posts)
To me, that means that the MINIMUM of those two values is evaluated and applied. So, if you didn't post anything in 2 weeks, you'd obtain an activity of 14. And if you posted 30, then you'd obtain an activity of 30.
You were right, it is indeed the MINIMUM between those two values where "time" is
If you have made 15 posts on your first 2-weeks-period and another 15 posts on your second 2-weeks-period, then it would be min(2*14 , 30) = 28. Your activity should be at 28 before the new 2-weeks-period ends.