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Math Help - 3 calculus things im stuck on

  1. #1
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    Joined
    Feb 2009
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    13

    Question 3 calculus things im stuck on

    formula y= (y0*L)/[y0+(L-y0)e^-kt]

    1.) when looking at a graph of a function, how do i estimate the value of k?


    2.) suppose that the growth of a population y=y(t) is given by the logistic equation y= (1000)/(1+999e^-.9t)
    when does the population reach 75% of the carrying capacity?
    so far i have:
    y= (750)/(1+999e^-.9t)
    e^-.9t= (750-y)/(999y)
    t= -.9ln[(750-y)/(999y)]
    but what do i plug in for y?


    3.)suppose that a population y(t) grows in accordance with the logistic model dy/dt= 50y-.0001y^2
    what is the value of k?
    for what value of y is the population growing most rapidly?
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  2. #2
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    Nov 2008
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    hmm is this first order differential equations?
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