That is the way it works, which I honestly do find to be a bit of a flaw. If you don't go in and close out the apps all the way (by holding any one of them down until they "wiggle" at which point you see the little minus sign where you can delete them), they will just keep adding up! At some point, I am sure this will necessarily impact either the memory or the storage space or both.
What you end up with is actually a quick launch bar with the things you use the most at the start... Quite useful I find...
Hope that helps.