The probability of a population going extinct by time t can be estimated by
p(t)= (a(e^((b-a)t)-1)/(b*e^((b-a)t)-a))^N
where a is the death rate, b is the birth rate (b does not equal a), and N is the number of individuals in the population at time t=0. Find and interpret p'(t)

Question

The probability of a population going extinct by time t can be estimated by 
p(t)= (a(e^((b-a)t)-1)/(b*e^((b-a)t)-a))^N 
where a is the death rate, b is the birth rate (b does not equal a), and N is the number of individuals in the population at time t=0.  Find and interpret p'(t)

anonymous · Answer

Eww, I'm not deriving that, but remember t is the only variable. Everything else looks to be a constant.

p'(t) should be the change in the probability of a population going extinct over time at any given time t.

anonymous · Answer

I used wolfram alpha and it gave me a long nasty answer, but that interpretation is what is important

anonymous · Answer

I mean, it shouldn't be that hard to derive it, just incredibly annoying and ugly. Almost as bad as inverting a 4x4 matrix not using the Gauss-Jordan method.