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Population Growth Differential Equations

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    A biologist prepares a culture. After 1 day of growth the biologist counts 1000 cells. After 2 days he counts 3000. Assuming a Malthusian model what is the reproduction rate and how many cells were present initially.

    2. Relevant equations

    [itex]P(t) = Ce^{rt}[/itex]

    3. The attempt at a solution
    [itex]P(1) = P(0)e^{r}[/itex]
    [itex]1000 = P(0)e^{r}[/itex]

    [itex]P(2) = P(0)e^{r2}[/itex]
    [itex]3000 = P(0)e^{r2}[/itex]

    Not sure how I am suppose to get the rate here.... or even start really..
  2. jcsd
  3. Feb 12, 2012 #2


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    That's a good start. It's all algebra now. Try solving for P(0) in both equations and then set them equal to each other.
  4. Feb 12, 2012 #3

    Ray Vickson

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    Maybe your notation is making it hard for you to see what is happening. If you set c = P(0) and x = exp(r), you have c*x= 1000 and c*x^2 = 3000. Surely you can get c and x from these!

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