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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 15 "Cobweb Diagrams" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 166 "This wor
ksheet illustrates the way in which Maple can be used to work with seq
uences.  The following cell defines a sequence representing a linear p
opulation model.  " }{TEXT 256 23 "Evaluate that cell now." }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "In
itialValue := 50:\n  Fcn := p -> 0.80 * p +1000:\n\n  pop :=\n     pro
c(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 sequen
ce you can print any of the terms of this sequence by evaluating a cel
l like the cell below.  " }{TEXT 257 60 "Evaluate that cell now and th
en 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 -1 141 "The next cell pro
duces a table showing the first 20 terms of this sequence.  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 80 "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.  T
he following cell does the job.  " }{TEXT 258 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 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 72 "Now you c
an use these Maple tools to study the sequences in this module." }}}}
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