TPE, TPE 3D and Photo Transit do not (at this time) use any background modes on iOS. Background Modes enable apps to perform tasks such as playing audio, supporting a voice call (VOIP), or reacting to location updates (e.g. recording a track in a GPS app). These activities consume battery power.
However, based on the way battery usage is reported in iOS, you may be led to think that our apps are in fact active in the background and consuming power. They are not, in fact - it's simply a subtlety of nomenclature, explained below (Battery Usage Reporting).
Rapid Battery Drain
As devices age, and with use, battery efficiency reduces. In some cases, the reported battery level becomes erratic and unpredictable, with rapid, large changes.
On my three year-old iPhone 6, the battery frequently drops from 37% to 1%. On plugging back into the charger, it typically jumps to 8% then back up to 37%.
When using an app that imposes a higher load on the CPU, and battery is in poor condition, you may observe rapid reductions in the indicated battery life. This can sometimes be a temporary effect: once the current draw on the battery is reduced again, the indicated remaining power returns to a higher level.
You can find tips on managing power usage in TPE 3D here.
Battery Usage Reporting
On iOS, you can check which apps are using your battery under Settings. You can find this information as follows. In the device's Settings app, scroll down and tap on Battery:
If you scroll down a little, after a couple of seconds, battery usage over the last 24 hours (or last 7 days) is shown. In the screenshot below, you can see that TPE has used 4% of battery in the last 24 hours, and Tweetbot (I'm a Twitter addict…) has used 15%.
Tweetbot shows "Background Activity", but TPE does not:
On tapping the clock, the total running time of each app is displayed. Notice that TPE now shows "12 min on screen - 18 min backgrounded". This does not mean that TPE is consuming battery due to background activity.
Rather, it, indicates that the app was still "in memory" on the device (i.e. backgrounded and inactive, but still running) for 18 minutes before being terminated by the user or operating system (e.g. to free up resources for other apps to run).