Lecture 4 -- Slide 10 Question

[Dan]

Hi Dan,

Slide 10 is copied and pasted here:

Q: A culture of yeast is grown for 10,000 generations (~2yrs). The
starting frequencies of the B allele and the b allele for gene X were
0.5 and 0.5. After the 10,000 generations, the allele frequencies were
0.4 (B) and 0.6 (b). Assuming no back-mutation, what is the mutation
rate from allele B to allele b? (If you don’t have a calculator, the
natural log of 0.8 is about -0.22)

Ans: pn = p0e-nμ. pn/p0 = e-nμ.
ln(pn/p0) = -nμ.
μ = ln(pn/p0)/-n = ln(0.4/0.5)/-10,000 = 2.2x10-5

Here is my question: In the first line of your answer, why did you
multiply p0e-nμ x pn/p0 (In other words, where did the 'pn/p0' term
come from? It was not in the previous lecture slide when you first
gave us the calculation?)

Help!! :)

[Lauren Wondolowski]

That line wasn't actually multiplied by pn/p0 (you're right - that wouldn't make sense!)
Rather, I think Dan was rewriting the first line in another way (by dividing both sides by p0) to more easily substitute in the values we have and solve. 
It could read:
Ans:
pn = p0e-nμ
pn/p0 = e-nμ
ln(pn/p0) = -nμ

μ = ln(pn/p0)/-n = ln(0.4/0.5)/-10,000 = 2.2x10-5