Question

Please help! I was trying to integrate this then i got stuck
dr/dt= 2r(1-r). So far i have: log(r)-log(1-r)+c=2t. I know I'm supposed to use e^log but i'm confused as to how to do it

Answer 1

hence
\[\ln\left(\frac{r}{1-r}\right) = 2t - c\]

Answer 2

Now take the exp of both sides and remember that exp(ln(a)) = a

Answer 3

I.e.,
\[ {r \over 1 - r} = Ae^{2t} \]

Answer 4

where A = e^-c

Now solve for r

Answer 5

Thank youuuu!