Growth of population/Logistic differential equation/Example/Properties of solution curves/Exercise

Consider the solutions

${}y(t)={\frac {g}{1+\exp(-st)}}\,$

to the logistic differential equation we have found in an example.

a) Sketch up the graph of this function (for suitable ${}s$ and ${}g$).

b) Determine the limits for ${}t\rightarrow \infty$ and ${}t\rightarrow -\infty$.

c) Study the monotony behavior of these functions.

d) For which ${}t$ does the derivative of ${}y(t)$ have a maximum (For the function itself, this represents an inflection point).

Create a solution