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Thread: [SOLVED] population growth differential equation problem

  1. #1
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    [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...?
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  2. #2
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    $\displaystyle \frac{dP}{dt} = .05(P - 9000)$

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

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

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

    $\displaystyle P(0) = 850$ ...

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

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

    proceed to answer the last two questions.
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  3. #3
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    thanks. that helped.
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