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                                                     Cobweb Diagrams

This notebook illustrates the way in which Mathematica  can be used to work with sequences.  The following cell defines a sequence representing a linear population model.  Evaluate that cell now.
;[s]
5:0,3;68,0;113,1;124,0;242,2;266,-1;
4:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;1,13,9,Times,1,12,0,0,0;
:[font = input; preserveAspect; ]
Clear[p]    (* Forget any old information *)
            (* about p.                   *)

p[1] := 50
p[n_] := 0.80 * p[n-1] + 1000
;[s]
3:0,0;12,1;89,0;132,-1;
2:2,12,10,Courier,1,12,0,0,0;1,12,10,Courier,1,12,65535,0,0;
:[font = special1; inactive; preserveAspect; ]
Now you can examine the population in any year, for example year 10, as illustrated in the cell below.  Evaluate that cell now.
;[s]
3:0,0;104,1;126,0;128,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
p[10]
:[font = special1; inactive; preserveAspect; ]
The cell below illustrates how Mathematica  can be used to print several years.  Evaluate that cell now.  Notice the 20 that indicates the number of years to be printed.
;[s]
6:0,0;31,1;42,0;81,2;106,3;169,2;170,-1;
4:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;2,13,9,Times,1,12,65535,0,0;1,13,9,Times,1,12,65535,0,65535;
:[font = input; preserveAspect; ]
TableForm[Table[{i, p[i]}, {i, 1, 20}]]
;[s]
3:0,0;34,1;36,0;40,-1;
2:2,12,10,Courier,1,12,0,0,0;1,12,10,Courier,1,12,65535,0,65535;
:[font = special1; inactive; preserveAspect; ]
The cell below illustrates how Mathematica  can be used to plot several years.  Evaluate that cell now.  Notice the 20 that indicates the number of years to be plotted.
;[s]
5:0,0;31,1;42,0;80,2;105,3;169,-1;
4:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;1,13,9,Times,1,12,65535,0,65535;
:[font = input; preserveAspect; ]
ListPlot[Table[{i, p[i]}, {i, 1, 20}],
         PlotJoined -> True,
         PlotRange -> {0, 5000}]
;[s]
3:0,0;33,1;35,0;101,-1;
2:2,12,10,Courier,1,12,0,0,0;1,12,10,Courier,1,12,65535,0,65535;
^*)