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Math Help - models for population growth!!..HELPP!!

  1. #1
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    models for population growth!!..HELPP!!

    The Pacific halibut fishery has been modeled by the differential equation:
    dy/dt=ky(1-(y/K) where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t(measured in years), the carrying capacity is estimated to be K=8 x 10^7 kg, and k= 0.71 per year.

    a) if y(0)=2 x 10^7 kg, find the biomass a year later.
    b) How long will it take for the biomass to reach 4 x 10^7 kg?

    HELPP!!
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    Quote Originally Posted by singh1030 View Post
    The Pacific halibut fishery has been modeled by the differential equation:
    dy/dt=ky(1-(y/K) where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t(measured in years), the carrying capacity is estimated to be K=8 x 10^7 kg, and k= 0.71 per year.

    a) if y(0)=2 x 10^7 kg, find the biomass a year later.
    b) How long will it take for the biomass to reach 4 x 10^7 kg?

    HELPP!!
    Basically you need a solution to the differential equation
    \frac{dy}{dt} = ky \left ( 1 - \frac{y}{k} \right )

    \frac{dy}{dt} = ky \left ( \frac{k - y}{k} \right )

    \frac{dy}{y(k - y)} = dt

    You can integrate the LHS using partial fractions.

    -Dan
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