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Expert: - 1/13/2009


Question
he speed of the wind increased exponentially. 10 minutes after sunrise, the windspeed was twice what it had been at sunrise. How many times faster will the wind be 15 minutes after sunrise?
Thanks for your help!

Answer
First, the problem states that the speed is increasing exponentially.
Second, it states that it doulbes in 10 minutes.
This would mean that in each of the first five minutes, it would be mulitplied by √2.  To check this out, 10 minutes is twice 5 minutes, so it would increase by √2 * √2, which is 2.  This is what the problem stated.  So in 15 minutes, that's three 5-minute intervals, so it would increase by √2^3 = √2√2√2 = 2√2.

That's the answer, but I think I could add a little more to the problem.  This would also mean that you probably would not one to be in the area after an hour had passed, since the increase would be over 12 5-minute intervals.  That would put it at √2^12 = 2^6 = 64 times as fast as at sunrise... but that increase is probably that fast only near the start.

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