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Logistic equations?

  1. Mar 22, 2015 #1
    Would really appreciate some help on this. Homework is due really early in the morning tomorrow, and I've been trying at this for a few hours to no avail.

    I have a logistic equation, (sorry, I just cannot use latex)
    dP/dT = (.00777777)P(9-P)
    (For P positive)

    Assume P(0)=2
    I must find P(65) or t=65
    I've solved this many times over and over, and I continuously get different answers. I'm not sure if I'm not even supposed to solve this, but here's what I try-
    I separate variables, and try to integrate this equation. Partial fractions, logarithms, etc, then I find C.
    I'm not posting the steps because I've done them at least ten times all different, somehow, but perhaps I'm not supposed to be solving for this????

    Anyhow I guess I try to find an equation for P(t) without derivatives- I get constants for C like 7/2, 2/7, other random numbers, not once does it ever work out well.


    This seems simple enough, just integrate the whole thing, but it really is just impossible for me. However one thing I do the same each time through is to separate variables, one side is 1/P(9-P) dP, the other side is 7/900 dt....
    After partial fractions, the rest just goes all weird.


    I have a second problem I hope someone can help with, I just took a picture of the problem.....
    http://postimg.org/image/tcscajp83/
    Yeah, I know it's standard here for the OP to show as much work as possible, but I kid you not I have spent hours on these problems and I cannot understand them. This second problem I cannot even begin to even try.

    Help would be much appreciated.
     
  2. jcsd
  3. Mar 23, 2015 #2
    I solved the first equation and I got the solution 9/[3.5 Exp(-7t)+1], at t=65 this is basically 9.

    For the second question you have to again solve the logistics equation with K=4300 (The upper case K), and P(0)=300.
    After you solve this, you will get P(t)= 12900/[40 Exp(-kt)+3]. Now the question states that the population tripled in the first year, this means that

    P(1)=3P(0)=900, so

    12900/[40 Exp(-k)+3]=900, this gives k=1.26113
     
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