Let me try to explain and see if it's close

The ETF share price and volume = assets in the fund. Based on the assets, 2x or 3x ETF can borrow 2 or 3 times to maintain the exposure to the underlying index. As the assets go up and down, re-balancing occurs. These ETFs do contain index futures and index options, but the "swap" seems to be the main tool in leveraging. So the decay is caused primarily by the calculations shown in 003's post (beta-slippage caused by leveraging + re-balancing). Option time decay is only secondary...
I'm new to this, just to share my understanding to see if it's close...