Insecticide A is said to be twice as potent as insecticide B if a concentration c of A is needed to kill the same proportion of insects as are killed by a concentraion 2c of insecticide B. In general A is $\displaystyle \lambda$ more times potent than B if a concentration of $\displaystyle \lambda c$ of B kills the same proportion of insects as does a concentration c of A.

The probability that an insect is killed by a concentration c of insecticide A is:

$\displaystyle \frac{exp(\alpha +\beta_{A}c)}{1+exp(\alpha + \beta_{A}c)}$

with the correspoding probability for insecticide B being

$\displaystyle \frac{exp(\alpha +\beta_{B}c)}{1+exp(\alpha + \beta_{B}c)}$

If A is twice as potent as B, what is the relation between $\displaystyle \beta_{A}$ and $\displaystyle \beta_{B}$?

What is the relation if A is $\displaystyle \lambda$ times as potent as B?

I'm not really sure where to start with this question, but I think with a hint I can finish the rest on my own.

Help much appreciated! Thanks.