That is what's happening - I'm not an electronics person but my vague understanding is modern li-ion batteries output e.g. 3.5v but actually hold between 2.x an

That is what's happening - I'm not an electronics person but my vague understanding is modern li-ion batteries output e.g. 3.5v but actually hold between 2.x and 4.x volts, and regulate power up or down. When it's full it's easier to push current through, when it's nearly empty it has to work a lot harder to supply power and consequently drains faster.