(*^

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                                       Exponential Models with Immigration
 
 The following cell illustrates the way in which Mathematica can be used to study exponential models with immigration.  Evaluate that cell now.
;[s]
6:0,0;39,3;74,0;126,2;137,0;197,1;221,-1;
4:3,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,0,0,0;
:[font = input; preserveAspect; ]
pop[1] := 2000
pop[n_] := 0.80 * pop[n-1] + 1000
:[font = special1; inactive; preserveAspect; ]
Now you can examine the population in any generation, for example generation 9, as illustrated in the cell below.  Evaluate that cell now.
;[s]
3:0,0;115,1;137,0;139,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
pop[9]
:[font = special1; inactive; preserveAspect; ]
The cell below illustrates how Mathematica  can be used to print several generations of a model.  Evaluate that cell now.
;[s]
5:0,0;31,1;42,0;98,2;121,0;122,-1;
3:3,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
TableForm[Table[{i, pop[i]}, {i, 1, 20}]]
:[font = special1; inactive; preserveAspect; ]
The cell below illustrates how Mathematica  can be used to plot several generations of a model.  Evaluate that cell now.
;[s]
4:0,0;31,1;42,0;97,2;121,-1;
3:2,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
ListPlot[Table[{i, pop[i]}, {i, 1, 20}],
         PlotJoined -> True,
         PlotRange -> {0, 10000}]
^*)