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The first plausible number I found in reasonable time that causes 0 bacteria on Day 3 - evening is 800, but to have exactly 0 bacteria at the end of D3 the starting number for the colony must be 875: Day 1 - morning: 1750 Day 1 - evening: 750 Day 2 - morning: 1500 Day 2 - evening: 500 Day 3 - morning: 1000 Day 3 - evening: 0
You can't do it this way because it's compounding on itself.
If you want to start backwards you have to do it like this (which I think was actually already posted in another method).
End of Day 3 = 0.....before losing 1000 = 1000, that morning before it doubled = 500
End of Day 2 = 500...before losing 1000 that night = 1500...that morning before doubled=750
End of Day 1 = 750...before losing 1000 that night = 1750...that morning before doubled = 875.
So 875 is the start, as said previously
My problem with this question though that it appears to asks for a certain number to start with, but in reality, there is a range which would still produce 0 at the end of day 3. if you start with 800 on day 1, you still end up with 0 at the end of day 3.
If you think of it as a range, then 875 > x > 750. If x has a value anywhere in that range, you will get 0 at the end of the 3rd day.
Lets start with x
Day Morning Evening
I x x-1000 II 2x-2000 2x-3000 III 4x-6000 4x-7000
------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.