Recent apps reside in memory but aren't taking up processing cycles or resources, thus aren't really using battery.iOS might seem like it is multitasking, but it isn't, at least for third party apps. It looks like it is because of the 'resume' feature of apps that allow them to hold a freeze state and resume right where they left off.
Rest assured, most apps actually close as soon as you hit home.
There are a few exceptions to this, namely first party apps, such as mail and music player, clocks, and so on (and of course notification centre). And a FEW apps can continue to be open if they use a handful of prescribed apis, such as voice recording (for example skype for calls), mapping Apis (for turn by turn) music playing etc. Some apps are allowed to remain open for up to 10 minutes if assigned a task duh as downloading a file.
Other than that apps are close when you hit the home button. The multitasking tray is nothing more than a glorified 'recently opened apps' list.