Here is the progression in number of users: There is a funny kink around April/May 2012... not sure what happened there...

There is an API to get statistics where the number indicates the days in the past relative to the current date. The stats 100 days ago are then:

http://www.biostars.org/api/stats/100/

There is a new API that is being added that lists both the users that joined on a given date and the posts and votes created on a given day, again relative to the current date. This is only exists in the sourcecode at this time. Alas it ended up more complicated and fragmented that I would like so I want to change that before making it public.

I'd be happy to take suggestions on what the API should look like and what the data should contain, perhaps a single request could return all relevant information for that day, perhaps changing the stats URL above to return something like this for a query of status 1000 days ago it:

{
    "date": "2010-03-05", 
    "new_users": [
        {
            "date_joined": "2010-03-05", 
            "id": 87, 
            "last_visited": "2011-11-08", 
            "name": "Khader Shameer"
        }, 
        {
            "date_joined": "2010-03-05", 
            "id": 88, 
            "last_visited": "2011-09-06", 
            "name": "Pierre"
        }
    ], 
   "new_posts": [
        {
            "answer_count": 0, 
            "author": "Jeroen Van Goey", 
            "author_id": 68, 
            "creation_date": "2010-03-05", 
            "id": 147, 
            "lastedit_date": "2010-03-05", 
            "parent_id": 35, 
            "rank": 2972.5582433999998, 
            "score": 0, 
            "title": "C: A: Which operating system do you prefer for bioinformatics?", 
            "type": "Comment"
        }
    ], 
    "post_count": 147,
    "user_count": 87
}