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So I've been trying to wrap my brain around this but it eludes me. The word problem would look something like this:

What is the minimum amount of seeds I need to buy to plant 850 seeds when only 60% of these planted seeds will produce a seed of their own. I can continue planting over and over until I reach my last seed.

I am looking for a formula I can use and plug into Excel - but a mathematical equation would be just great!

Thanks

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You are just summing a geometric series. If you start with $n$ the next generation gives you $0.6n$, the one after that gives $0.6^2n$, then $0.6^3n$ so you want $$850=n(1+0.6+0.6^2+0.6^3+\ldots )=\frac n{1-0.6}\cdot 850\\n=0.4\cdot 850=340 $$

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  • $\begingroup$ that's awfully optimistic about the farmer's ability to successfully plant a fraction of a seed. $\endgroup$ – Zackkenyon Jun 21 '18 at 21:27
  • $\begingroup$ @Zackkenyon: that is true. I think my approach is in the spirit of the question. I took the $0.6$ as a probability that each seed produces another. We could round up a bit to cover. $\endgroup$ – Ross Millikan Jun 21 '18 at 21:37
  • $\begingroup$ @Zackkenyon thanks for not providing any helpful feedback. The question isn't based on a real world scenario. $\endgroup$ – Louis Craig Jun 22 '18 at 20:03
  • $\begingroup$ @Ross that works! I don't quite see how you got from the first part 850=n(1+0.6+0.62+0.63+…) to this =(n/(1−0.6))*850 could you explain a little more in depth? $\endgroup$ – Louis Craig Jun 22 '18 at 20:07
  • $\begingroup$ Look up geometric series on Wikipedia. It is like converting a repeating decimal to a fraction. $\endgroup$ – Ross Millikan Jun 23 '18 at 4:34
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1 seed grows 2.5 seeds on average, so divide 850 by 2.5 and you have your answer. You can use infinite geometric series formula to find expected number of seeds for 1 seed.

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  • $\begingroup$ No one seed grows 0.6 seeds. $\endgroup$ – Louis Craig Jun 22 '18 at 19:59

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