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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 30 "Sequences -- Population \+
Models" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
210 "This worksheet illustrates the way in which Maple can be used to \+
work with sequences.  The following cell defines a sequence representi
ng a population that is growing exponentially at the rate of 4% per ye
ar.  " }{TEXT 256 23 "Evaluate that cell now." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "InitialVal
ue := 100:\n  Fcn := p -> 1.04 * p:\n\n  pop :=\n     proc(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 sequence you can pri
nt any of the terms of this sequence by evaluating a cell like the cel
l below.  " }{TEXT 257 60 "Evaluate that cell now and then go on to th
e 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 produces a table sho
wing the first 20 terms of this sequence.  " }{TEXT 258 64 "Evaluate t
he next cell now and then go on to the following cell." }}{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 a
nd then go on to the following cell." }{TEXT -1 1 "\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "plot([seq([n, pop(n)], n = 1 .. 20)
], \n        year = 1 .. 20, title = `Population`);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Now you can use
 these Maple tools to answer the questions posed in this module." }}}}
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