anonymous
  • anonymous
Let y(t) be the population of certain species at time t. (a). Write down the logistic equation that describes the dynamics of the population, assuming an environmental carrying capacity K and an intrinsic growth rate r. (b). Solve the equation for y(t) if K = 1000 and r = 0:1 per year. (c). How long does it take for the population to be doubled if the initial population is 100
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
(a) This is somewhat vague, and includes more variables than the parameters, but it's what I remember from partial fraction integration:\[y(t) = K/(A-Ce^{-rt})\] where A and C are constants.
anonymous
  • anonymous
The exam review actually says that the answer to (a). is dy/dt = ry(1-(y/k)) and the answer to (b) is 1000C/(e^(-0.1t) - C) while (c) is 8.1 years I'm trying to figure out how to go about actually doing it.. but I can't find a decent enough explanation anywhere. Ahh I'm in trouble for this test.
anonymous
  • anonymous
Basically what the review says and what I said are essentially the same, but I gave it in a solved form; it was asking for the "dynamics" or the equation stating the rate of change. You want to look up "Integrating by Partial Fractions" if solving the differential equation is difficult.

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anonymous
  • anonymous
I'll try that, thanks.

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