Logistic Equation

The simple model

This code should be reminiscent of the Fibonnaci sequence discussed above.

Clear[pop,n,R,K];
pop[0]=50;
R=2.7;
K=100;
pop[n_]:=pop[n]=pop[n-1]*(R(1-pop[n-1]/K)+1);

The Table command can be used to create a list of data.  Here the data consists of ordered pairs.  We give the list the name cranes so that it can be used later.

logistic=Table[{n,pop[n]},{n,0,30}]

The suffix //TableForm can be used to put the data in a nice table format.

logistic//TableForm

Plot[{x, x*(R (1 - x/K) + 1)}, {x, 0, 200}];

Dt[x*(R (1 - x/K) + 1), x]

slope[x_] := 1+R (1 - (x/K))-R x/K;

Abs[slope[K]]

ListPlot[logistic,PlotJoined->False,AxesLabel->{"Years", "Population"},PlotRange->{50,150}];