I tihnk that really depends on the couple, what kind of relationship they're each looking for (long-term, casual, FWB), how well things are going between them, and when the topic of being exclusive comes up.
When he asks me! I don't really like dateing, I perfer hanging out because I don't have the time to date. I have school, sports practices and just life in general. I like hanging out between classes, an hour before waterpolo practice. That kind of stuff. Maybe a actual date when the day is special, though! :)
I would say within six weeks you know whether or not you're going to stick with this person. That's what, two months? Presuming that you're interested in each other and communicating regularly, that doesn't leave too much time and energy for dating other people. If your focus on the person (during your free time) is "lazy" and you find yourself to still be curious about dating other people, then it's not meant to be an exclusive relationship, not matter how many dates you've been on.
If I like a girl enough to want to take her out, I'm exclusive to her. Now I'm not the kind of guy who's gonna try to pick up girls and actually get to know them through a date. I get to know them first, then see if I want to date them.