The activity number is determined in this way:
time = number of two-week periods in which you've posted since your registration
activity = min(time * 14, posts)

Rough summary of what this means: If you post once per day on average, then you will eventually get the maximum number of activity points that you can get. Posting more than once per day on average is useless for increasing activity. The maximum number of activity points you can get is 1 per day, but your activity score only updates every two weeks. Therefore, it will take about 100 days to get 100 activity if you post once per day on average.

Activity is updated every hour.

The new membergroup limits work like this:

Group	Requirement
Brand New	0 posts
Newbie	(none)
Jr. Member	activity: 30
Member	activity: 60
Full Member	activity: 120
Sr. Member	activity: 240
Hero Member	activity: 480
Legendary	occurs randomly between 775 and 1030 activity

I'm not 100% sure that the membergroups work correctly. Tell me if you see any bugs.