The lily pads that double every day

Question

In a lake there is a patch of lily pads. Every day the patch doubles in size. It takes 48 days for the patch to cover the entire lake.

How many days does it take for the patch to cover half of the lake?

Accepted Answer

47 days. Backwards. On day 48 the patch covers the whole lake. It doubled from the previous day, so on day 47 it covered half the lake. On day 46 it covered a quarter, on day 45 an eighth, and so on. Why 24 is tempting and wrong. Halving the time feels like halving the coverage, but that is how linear growth works, not doubling. With doubling, the patch on day 24 covers only 1 divided by 2 to the 24 of the lake, about one sixteen-millionth: essentially invisible. The lesson about exponentials. Almost all of the growth happens at the very end. The patch spends 40 of its 48 days covering less t…

The lily pads that double every day

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