Stop Closing Your iPhone's Background Apps
gizmodo.com
gizmodo.com
The CPU uses real power when it runs at full speed. The cost scales with the number of reopenings, though, which may be very low.
BTW, looking at the Android history makes me doubt that advances in battery will lead to background apps. Lead to lighter devices, yes, longer battery lifetime, yes, but background apps?
I suspect the same applies for certain connected devices.