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

Question

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

anonymous · Answer

(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 · Answer

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 · Answer

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.

anonymous · Answer

I'll try that, thanks.