Riddle of the Lily Pads

There is great truth in the oft-quoted riddle of the lily pads. A pond (a lake, an ocean, all apply) starts with a single lily pad. Each pad doubles per day; the pond will be full in thirty days. When is the pond only half full? On the twenty-ninth day. After the next day, the thirtieth, further growth is so fast it will, if somehow continued, overwhelm the pond and everything in it in a matter of hours.