Firstly, apologies if I'm going over old ground, but I can't see any mention of this in the Google document, so hopefully it's new.
I found something interesting by accident last night. I downloaded one of those battery/system status apps, just because it was free (ActMonitor), and it includes a function which shows which programs are running.
Initially I had nothing much running, and it said that it was running itself, also MobileSMS and MobileMail (it doesn't show system processes).
I opened a few more apps to see if they'd show up, and they did. I got up to about 10 running.
Then I opened a load more, and opened ActMonitor again. 4 programs running. According to the double-clicked home button there were about 20 in the background, but ActMonitor told me there were 4. It also said there was a lot more memory free than there had been when there were 10 running.
It seems to me that, if ActMonitor is to be believed, the number of apps running in the background according to the pretty double-click screen (unless it's very small) bears no resemblance to what's really running, most of them are shut.
I don't know what "wired" memory (currently showing as 300MB), "active" (125MB) and "inactive" (55MB) are (I can guess at what "free" is), but it shows them too. Is "inactive" memory what holds app information in the background?
I figure there are three options:
1) iOS7 is incredibly memory-hungry and doesn't allow space for apps to be stored in the background (is the 300MB, which sometimes drops to about 170MB the size of iOS in memory? Isn't that huge?)
2) the amount of storage needed to keep apps in their running state is a lot higher in iOS7 than previously
3) there's something very inefficient about memory management, and instead of using it to store app data in the background it kills the apps, rather than perhaps killing some unnecessary system stuff like in earlier versions?