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Ugh! Logistic differentiation

  1. Sep 19, 2007 #1
    1. The problem statement, all variables and given/known data

    This problem is driving me crazy because it seems so simple yet I can't get the right answer. We're looking for how long it takes for the biomass of halibut to get within 10% of carrying capacity (look below).


    2. Relevant equations

    We have to use this formula: y(t)= 8x10^7/(1+3e^-.71t)

    3. The attempt at a solution

    I don't even know. How do I find t without knowing y(t)? Everyone I've asked so far has said, "Just plug in". Just plug in what? I know M needs to be changed, and that's about it. The correct answer is 4.6. I'm so confused. Help please?
     
  2. jcsd
  3. Sep 19, 2007 #2

    Hurkyl

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    What are y and t?
    What is "carrying capacity"?
    What is M?
     
  4. Sep 19, 2007 #3
    M is carrying capacity (10% of 8x10^7), t is time (which I'm looking for), and y(t) is the population. I'm confused because I don't have t or y(t).
     
  5. Sep 19, 2007 #4

    Hurkyl

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    Well, how does biomass relate to anything? Proportional to population, I suppose? You should name the constant of proportionality, if it's going to be relevant.

    The carrying capacity is 10% of 8 * 10^7? That seems an odd definition; why the 10%? Anyways, I suppose from context that it's a measure of biomass.

    Well, you know what 10% of the carrying capacity is. (right?) That seems like a place to start.
     
    Last edited: Sep 19, 2007
  6. Sep 19, 2007 #5
    Biomass is just the math book's way of saying population.

    So I'm looking for the time at which population, y(t), is within 10% of carrying capacity (M, which equals 8.7x10^7). My problem is that I don't know y(t), so how do I find t? Should I plug in, say, t=0 and find y(0), then use that to find the other t? That doesn't make sense to me, since population is changing, but it's the only way I can phathom.
     
  7. Sep 19, 2007 #6

    Hurkyl

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    Well, you do know a the value of

    y(the time when the biomass is within 10% of the carrying capacity),

    right?



    I guess since you're trying to answer "how long", you need a starting time and an ending time. The ending time would presumably be

    the time when the biomass is within 10% of the carrying capacity,

    does the problem give an indication of the starting time? With no other information, I'd probably guess that you start waiting when time = 0.
     
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