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Exponential worm farm math problem?
A farmer breeds a strain of self-reproducing worms. Each worm produces its first offspring at the age of two weeks and continues to produce one offspring each week there after. He started breeding these worms just over 20 weeks ago, and assuming he had exactly one newborn worm at that time, how many worms does he have now? (Assume that no worm has died.)
1 Answer
- 1 decade agoFavorite Answer
The number worms follows the Fibanacci sequence!
http://en.wikipedia.org/wiki/Fibonacci_number
An informal proof goes like this. Every new period, you have the same number of worms that you had before since no worm has died, so you add the value of the last period. You then add the value of two periods ago since those are the number of worms who can reproduce (since those are the number of worms who have been around for 2 weeks or more).
So suppose that you figure out the sequence goes 1,1, 2,3,5, 8.... you figure out the next number adding the previous 2 numbers: 5 and 3, 5 because that is the number of existing worms, and 3 since that is number of worms who can multiply, so you get 13 for your next number. You then add 5 and 8 to 13 to get the next number which is 26.
After 20 weeks you have, 13530 worms (the 21st value of the fib sequence).
