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Everyday,double in size. If it takes 48 days for the patch to cover the entire lake, how many days would it take to cover half of the lake?

a patch of lily pads double every day

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47 days.

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Ok I am no math whiz but if you are saying it takes 48 days to cover the entire lake with the patch then wouldn't it take half that many days to cover half of the lake. I am going to say it would take 24 days to cover half the lake.

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47 days is the answer. Gotta work it backward.
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Waldorff is correct. The growth of the patch of lily pads is exponential. If every day the patch doubles in size, that means that every day the patch is half the size it will be next the day. If on day 48 it takes up the whole lake, on day 47 it will take up half, and on day 46 it will take up a quarter, etc.

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It's a trick. Even the world's largest lake is not big enough to hold that big of such an invasive Lilly Pad patch.