Posted: 7/18/2005 6:23:34 AM EDT
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I have a question for mathematically inclined folks here… My boss sends out daily messages like the following. Mostly, pretty generic stuff intended to “inspirational”. Today I rec’d the following: Thought of the Day It is said that scientific knowledge is growing at an exponential rate. To appreciate what that means, consider the story of a farmer who brought his horse to be shod and asked what it would cost. The blacksmith said he would charge a penny for the first nail, 2 cents for the second, 4 cents for the third, and so on. The farmer, innocent of mathematics, agreed. For eight nails in each shoe, or 32 nails altogether, his bill came to $42,949,672.95. An exponential rate of growth is a fearsome thing. -From "Bits and Pieces" For kicks, I decided to “do the math” on my desk calculator. When I do the calculation, doubling each number to get the next, I calculate the total to be $21,474,836.48. It appears that the $42,949,672.95 figure is the result of 33 “nail” calculations, not 32. Did I calculate the problem incorrectly? Is this really an “exponential” calculation? Thanks! |
No, I didn't do that... that is probably why I came up with a different result. When/if our system comes back online, I'll try to do this on Excel so I don't have to add up all the numbers. Thanks! |
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I used excel and got 42949672.95 edit: 0.01 0.02 0.04 0.08 0.16 0.32 0.64 1.28 2.56 5.12 10.24 20.48 40.96 81.92 163.84 327.68 655.36 1310.72 2621.44 5242.88 10485.76 20971.52 41943.04 83886.08 167772.16 335544.32 671088.64 1342177.28 2684354.56 5368709.12 10737418.24 21474836.48 (sum) $42,949,672.95 |