1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential equations help.

  1. Feb 19, 2008 #1
    Hey, everyone. I've been doing my Calculus II homework, and I've been trying these two problems for the past few hours, but I can't even seem to get started on them. A friend of mine recommended I try here because you guys are awesome.

    1. The problem statement, all variables and given/known data
    The Gompertz equation
    dP/dt = P(a - b ln(P))
    where a and b are positive constants, is another model of population growth.
    a) Find the solution of this differential equation that satisfies the initial condition: P(0) = p(sub(0))
    b) What happens to P(t) as t -> infinity?
    c) Determine the concavity of the graph of P


    2. The attempt at a solution

    dP/dt = P(a - bQ)
    where Q = ln(x)​



    1. The problem statement, all variables and given/known data

    the differential equation
    dP/dt = P(10^-1 - (10^-5)P)
    models the population of a certain community. Assume P(0) = 2000 and time t is measured in months.
    a) Find P(t) and show that lim t -> infinity exists
    b) Find the limit


    2. The attempt at a solution

    I do not even know where to start on this. Any help at all would be nice.
     
  2. jcsd
  3. Feb 19, 2008 #2
    Write it as
    [tex]\frac{d\,P}{P\,(a-b\,\ln P)}=d\,t[/tex]
    and set [itex]\ln P=u[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Differential equations help.
Loading...