# Thread: [SOLVED] population growth differential equation problem

1. ## [SOLVED] population growth differential equation problem

Consider a population p of a field mouse that grows according to the following differential equation: dp/dt = 0.5p - 450

* find the time at which the population becomes extinct if p(0) = 850
* find the time of extinction if p(0) = p(sub zero), 0 < p(sub zero) < 900
* find the initial population p(sub zero) if the population is to become extinct in 1 year

im not sure how to find the time given the equation is in terms of population. can anyone help, please...?

2. $\frac{dP}{dt} = .05(P - 9000)$

$\frac{dP}{P - 9000} = .05 \, dt$

$\ln(P-9000) = .05t + C$

$P = 9000 + Ae^{.05t}$

$P(0) = 850$ ...

$P = 9000 - 8150e^{.05t}$

set $P = 0$ , solve for $t$

proceed to answer the last two questions.

3. thanks. that helped.