SOLUTION: Cell Division: One leukemic cell injected into a healthy mouse will divide into two cells in about 1/2 day. At the end of the day these two cells will divide again, with the doub

Question 168807: Cell Division: One leukemic cell injected into a healthy mouse will divide into two cells in about 1/2 day. At the end of the day these two cells will divide again, with the doubling process continuing each 1/2 until there are 1 billion cells, at which time the mouse dies. On which day after the experiment is started does this happen?
I'm having a horrible time coming up with a formula for this problem.
I would appreciate any help you can give me on this one.
Thank you so much, ahead of time!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Cell Division: One leukemic cell injected into a healthy mouse will divide into two cells in about 1/2 day. At the end of the day these two cells will divide again, with the doubling process continuing each 1/2 until there are2^x 1 billion cells, at which time the mouse dies. On which day after the experiment is started does this happen?
I'm having a horrible time coming up with a formula for this problem.
I would appreciate any help you can give me on this one.
Thank you so much, ahead of time!
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The divisions double the number of cells, so the number will be a power of 2, as in 2, 4, 8, 16, 32 etc.
The power of 2 closest to "about a billion" is 2^30 = 1,073,741,824. BTW, this is also a Giga, as in a Gigabyte of RAM, or space on a hard drive.
Anyway, it will take 30 divisions, so that's 30 half-days, or 15 days.
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If you don't happen to know that 2^30 is apx a billion (some people don't):
2^x = 1,000,000,000
x*log(2) = log(1000000000)
x*0.30103 = 9
x = 29.9 half days

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