[SOLVED] population growth differential equation problem

**mathprincess24** · February 9th 2009, 04:10 PM

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...?

**skeeter** · February 9th 2009, 05:29 PM

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

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

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

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

$P(0) = 850$ ...

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

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

proceed to answer the last two questions.

**mathprincess24** · February 10th 2009, 05:24 AM

thanks. that helped.

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