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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 28 "Sequences -- Logistic Mo
dels" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 110 "
The next cell illustrates the way in which models like those studied i
n this module can be defined in Maple.  " }{TEXT 256 16 "Evaluate it n
ow." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 163 "  InitialValue := 100:\n  Fcn := p -> 2.0 * (1 - 0.0
01 * p) * p:\n\n  pop :=\n     proc(n)\n        if n = 1 then InitialV
alue else Fcn(pop(n-1)) \n        fi \n     end:" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 1 "\011" }}{PARA 0 "" 0 "" {TEXT -1 143 "Now that Mapl
e \"knows\" how to compute this sequence you can print any of the term
s of this sequence by evaluating a cell like the cell below.  " }
{TEXT 257 60 "Evaluate that cell now and then go on to the following c
ell." }}{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 showing th
e first 20 terms of this sequence.  " }{TEXT 258 64 "Evaluate the 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.  T
he following cell does the job.  " }{TEXT 259 53 "Evaluate it now and \+
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 M
aple tools to answer the questions posed in this module." }}}}{MARK "0
 0 0" 28 }{VIEWOPTS 1 1 0 1 1 1803 }