I have heard here the minimum amount of time you should have a question open until you accept an answer is one day, but I was wondering about how long it takes until the question will most likely not receive any more attention?
This number would help me decide when it is time to accept an answer.
I don't think there's any readily available data on this, but it'd almost certainly be possible to use SEDE (Stack Exchange Data Explorer) to gather statistics on how many answers, or how large a percentage of answers, are given within some given time frame of asking the question. Net voting statistics are there too, so could be factored in if desired. I'm not up to doing that right now, though.
The general recommendation, as you have found, is to wait at least 24 hours before accepting an answer. This really isn't a hard-and-fast rule by any means, but simply based on that:
That last piece is actually important. Been resolved to the asker's satisfaction.
Assuming that you get an answer that solves your problem, you should ideally accept that answer. If you get an answer that solves your problem within an hour, then you are absolutely within your rights to accept that answer immediately, or within a day or two. You should not, however, accept an answer just because some arbitrary "sufficient" amount of time has passed since you asked the question. If the question hasn't been resolved to your satisfaction, go right ahead and not accept any answer, even if you have received several. Maybe even set a bounty and explain what you are looking for that the existing answers don't provide.
Go ahead and accept an answer if you are happy with it and feel that you don't need further ones, but don't feel pressured to do so; and realize that by accepting an answer, you reduce the chances of getting further answers. Exactly when to make that cut-off point is a trade-off really only the person asking a question can do. We can't do it for you, and even providing guidelines (beyond the very general ones, such as above) would be difficult.
If you want a rough indication of how many people have seen your question, look at the views count near the top right of the question page (assuming a desktop web browser). That's a better indication for how much activity it has seen than merely the amount of time that has passed since it was posted.
There are many regulars on WorldBuilding.SE living all around the globe in different timezones. To give everyone a chance to look at your question you should at least wait 24 hours before accepting an answer.
The reasons mainly involve the quality and amount of answers you get.
Some people are discouraged when they see a question already has an accepted answer - the OP found the solution to his problem already, so why should I care and try to help him if he doesn't need any more help?
Furthermore people check out the question and the answers. They check whether the given facts make sense or whether some details need more work. This helps to increase the quality of the answers you receive.
All in all nobody can force you to accept an answer or not. It's completely, absolutely, totally your decision and yours alone when to accept, what to accept and whether you want to accept at all or not.
Relevant Meta discussions:
Please wait at least 24 hours before Accepting an answer
Let's be careful about accepting answers early
Should moderators mark a high voted answer as the accepted answer after a while?
Can I choose two answers for my question as the accepted answer(s)?
This depends on a lot of things.
Was it in the Hot Network Questions?
Did you post it on the weekends?
Is it referenced in other questions?
Did you or someone else put a bounty on it?
Did someone revive an old question with an edit or a new answer?
Are there already good, in-depth answers?
Did you recently edit the question?
Was the question put on hold and later reopened?
Are there new comments asking for clarification?
Is the view/vote count already pretty high for the type of question you are asking?
Just wait at least 24 hours and decide when you think nothing is happening anymore. Maybe a week? After two days or so you get a little message on your question tab, but in my personal experience I've mostly waited at least a week. Sometimes longer if one or more of the things above were true.
But, again: if you haven't got a satisfying answer you don't have to accept an answer. Nobody can force you or tell you what's right about accepting. These are just a few tips to increase the visibility of your question and thereby increase the amount and quality of the answers you receive.
