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Diffy-Q question

  1. Feb 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Consider the population model
    dP/dt = -P^2/50 + 2P

    for a species of fish in a lake. Suppose it is decided that fishing will be allowed, but
    it is unclear how many fishing licenses should be issued. Suppose the average catch
    of a fisherman with a license is 3 fish per year (these are hard fish to catch).

    (a) What is the largest number of licenses that can be issued if the fish are to have
    a chance to survive in the lake?

    (b) Suppose the number of fishing licenses in part (a) is issued. What will happen
    to the fish population-that is, how does the behavior of the population depend
    on the initial population?

    (c) The simple population model above can be thought of as a model of an ideal
    fish population that is not subject to many of the environmental problems of an
    actual lake. For the actual fish population, there will be occasional changes in
    the population that were not considered when this model was constructed. For
    example, if the water level increases due to a heavy rainstorm, a few extra fish
    might be able to swim down a usually dry stream bed to reach the lake, or the
    extra water might wash toxic waste into the lake, killing a few fish. Given
    the possibility of unexpected perturbations of the population not included in
    the model, what do you think will happen to the actual fish population if we
    allow fishing at the level determined in part (b)?

    3. The attempt at a solution

    I am not sure how to start part a. Should I model the equation first like so :
    dp/dt = -P^2/50 + 2P - 3C

    Where C is license?
     
  2. jcsd
  3. Feb 20, 2010 #2
    Figured it out, thanks for looking.
     
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