## Question

How many times must a fertilised ovum divide to form a normal term baby? Does this account for the placenta and apoptosis? How many cells are in a newborn? How fast is the cell division curve in each month?

## Answer

**Chris Smith got out a paper and pen to work through this one...**

Chris - Well, actually, this comes down to pretty simple maths. Because, if we think about it, a single egg divides into two, and one cell becomes two, and then those cells each divide in half again. So two splits to make four and those four cells split themselves in half and they become eight. And then those eight cells split in half and you get 16 and then 32 and this grows exponentially; and that means we can write an equation to represent that growth where you say 2 to the power of n, which is the number of divisions, equals X cells. So, if we want to know what n is (how many divisions), we need to know how many cells. Well a baby contains, probably, a couple of trillion cells. So, therefore 2 to the power of n divisions must equal about 2 trillion.

So how do we find out what n is? Well you can do this using logarithms. So if we take the natural logarithm of both sides of the equation, you actually then get n x ln2 = ln(2 trillion). If we then divide both sides by the natural logarithm of 2 (ln 2) you get:

ln (2 x 10^{12}) / ln2 and that's actually 28.34 divided by 0.693. That's about 41.

So, what that tells you is that a single cell only has to divide about 41 times to end up with 2 trillion cells that would make up a baby! It's not as many as you might think, is it?

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