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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 48 "Sequences -- Exponential
 Models with Immigration" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 58 "The next cell defines a model like those in this m
odule.  " }{TEXT 256 15 "Evaluate it now" }{TEXT -1 1 "." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "  I
nitialValue := 100:\n  Fcn := p -> 0.80 * p + 200:\n\n  pop :=\n     p
roc(n)\n        if n = 1 then InitialValue else Fcn(pop(n-1)) \n      \+
  fi \n     end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 143 "Now that Maple \"knows\" how to compute this sequ
ence you can print any of the terms of this sequence by evaluating a c
ell like the cell below.  " }{TEXT 257 60 "Evaluate that cell now and \+
then go on to the following cell." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "pop(10);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "The next cell prod
uces a table showing the first 20 terms of this sequence.  " }{TEXT 
258 64 "Evaluate the next cell now and then go on to the following cel
l." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 86 "for k from 1 to 20 \n      do printf(`%4d %10.4f`, k,
 pop(k));\n      print();\n      od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "Maple can also produce a graph \+
showing this same data.  The following cell does the job.  " }{TEXT 
259 53 "Evaluate it now and then go on to the following cell." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 86 "plot([seq([n, pop(n)], n = 1 .. 20)], \n        year = 1 .. 20, \+
title = `Population`);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Now y
ou can use these Maple tools to answer the questions posed in this mod
ule." }}}}{MARK "0 0 0" 48 }{VIEWOPTS 1 1 0 1 1 1803 }