1. ## limits

Consider a population of a species for which each individual has a constant probability, b, of producing a new individual (birth) and a constant probability, d, of going extinct (death). The extinction probability as a function of time, t, can be approximated by (b not equal to d ):

P(t)= d((e^(b-d)t)-1)/(be^(b-d)t)-d

Compute the limit P(t) for (t) approaches infinity if 1) b>d and 2)b<d

2. Originally Posted by math123456
Consider a population of a species for which each individual has a constant probability, b, of producing a new individual (birth) and a constant probability, d, of going extinct (death). The extinction probability as a function of time, t, can be approximated by (b not equal to d ):

P(t)= d((e^(b-d)t)-1)/(be^(b-d)t)-d

Compute the limit P(t) for (t) approaches infinity if 1) b>d and 2)b<d

It is hard to read the model's equation. Is this anything close to what it is supposed to look like?

$P(t)= d \frac{e^{(b-d)t}-1}{be^{(b-d)t}} -d$