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Maths people - ??

If we start off with one cell which goes on to divide 84 times, how many cells will there be after the final division?? Surely after it divides once we have 2 cells and since one division had already taken place, it’s 2^83?
I am pretty sure it is 2^84. We can simplify the problem by considering only dividing three times. After one division you have two cells, after two, 4 cells, and after three, 8 cells - which is 2^3. It follows that if you divide 84 times, you produce 2^84 cells.
Original post by anosmianAcrimony
I am pretty sure it is 2^84. We can simplify the problem by considering only dividing three times. After one division you have two cells, after two, 4 cells, and after three, 8 cells - which is 2^3. It follows that if you divide 84 times, you produce 2^84 cells.


Unfortunately this makes complete sense to me which means I’ve lost those two marks in my biology exam
Original post by Wolfram Alpha
If we start off with one cell which goes on to divide 84 times, how many cells will there be after the final division?? Surely after it divides once we have 2 cells and since one division had already taken place, it’s 2^83?


No because the first division needs to be included in the 84.

for example

if a cell divides 5 times
2^5 +32
after the first division there is 2 cells
after the second division there is 4 cells
after the third division there is 8 cells
after the fourth division there is 16 cells
after the fiftch division there is 32 cells

do you see what i mean?
Original post by Wolfram Alpha
Unfortunately this makes complete sense to me which means I’ve lost those two marks in my biology exam


=(

On the bright side, 2^84 is somewhere around 10^25, and using the average weight of a cell, that would be in the order of thousands of tons of biomass - so the question was completely unrealistic.
Original post by 13dsaivaines
No because the first division needs to be included in the 84.

for example

if a cell divides 5 times
2^5 +32
after the first division there is 2 cells
after the second division there is 4 cells
after the third division there is 8 cells
after the fourth division there is 16 cells
after the fiftch division there is 32 cells

do you see what i mean?


Does this mean 2^83 is correct?
@Zacken

?
Original post by Wolfram Alpha
Does this mean 2^83 is correct?


No sorry i don't think so x

because 5^4 would = 16 and that is not the answer to 5 divisions
exams are bi*ch sometimes...
This sounds like such a nice question. Shame my biology paper included stuff that wasn’t included in the specification :frown:
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Notnek
21
Original post by Wolfram Alpha
If we start off with one cell which goes on to divide 84 times, how many cells will there be after the final division?? Surely after it divides once we have 2 cells and since one division had already taken place, it’s 2^83?

There are 2 cells after the first division, then 4 after the second etc. so your sequence is

2, 4, 8, ...

Then the number of cells after the nth division will be

2^n

So the answer is 2^84
Original post by //Destiel
This sounds like such a nice question. Shame my biology paper included stuff that wasn’t included in the specification :frown:


Mate that was like the only nice question and seems like I've even f*cked that up! What exam board do you do?
Original post by Notnek
There are 2 cells after the first division, then 4 after the second etc. so your sequence is

2, 4, 8, ...

Then the number of cells after the nth division will be

2^n

So the answer is 2^84


I've aceepted it's 2^84 but to b honest I still don't get why :biggrin: becausxe surely when we have 2 cells, 1 division has already occurred so we only have 83 divisions left? Can't believe I'm an A Levels maths student :colondollar:
Original post by Wolfram Alpha
If we start off with one cell which goes on to divide 84 times, how many cells will there be after the final division?? Surely after it divides once we have 2 cells and since one division had already taken place, it’s 2^83?


Yeet
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Notnek
21
Original post by Wolfram Alpha
I've aceepted it's 2^84 but to b honest I still don't get why :biggrin: becausxe surely when we have 2 cells, 1 division has already occurred so we only have 83 divisions left? Can't believe I'm an A Levels maths student :colondollar:

Yes that's right but once one division has taken place you have 2 cells not 1 so if you like your first term in the sequence is 2. Then if you multiply 2 by 2 83 times you get

2×283=2842 \times 2^{83} = 2^{84}.

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