w1d - Douglass Houghton Workshop Section 1 Mon Worksheet...

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Douglass Houghton Workshop, Section 1, Mon 9/19/11 Worksheet Dauntless 1. The Saga of Michael Phelps: Conclusion Last time we found that Michael Phelps can always make himself dryer by splitting his towel, but there’s a limit to how dry he can get. In particular, here are the numbers for not splitting the towel at all and for splitting it into 10,000 pieces: Towel Size .25 .5 1 2 3 4 wetness (1 piece) 0.8000 0.6667 0.5000 0.3333 0.2500 0.2000 wetness (10,000 pieces) 0.7788 0.6065 0.3679 0.1354 0.0498 0.0183 Cutting into more than 10,000 pieces doesn’t seem to make much difference. So for each towel T , there is a wetness N ( T ) after normal toweling, and there seems to be a “magic number” M ( T ), which is the limit to how dry Michael can get by splitting the towel. (a) Make a graph with towel size on the x -axis and wetness on the y -axis. Plot the points you have for N ( T ), the result of normal toweling, and M ( T ), the result of split towelling. (b) What’s the formula for N ( T )? (We found this last week).
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