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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 13 "Linear Models" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 182 "This worksheet
 illustrates the way in which Maple can be used to work with sequences
.  The following cell defines a sequence representing the first popula
tion model in this module.  " }{TEXT 256 23 "Evaluate that cell now." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 149 "InitialValue := 50:\n  Fcn := p -> 0.80 * p +1000:\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 print any of the terms of this sequence by evalu
ating a cell 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 -1 141 "T
he next cell produces a table showing the first 20 terms of this seque
nce.  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 80 "for k from 1 to 20 \n    do printf(`%4d %10.4f`, k, p
op(k));\n    print();\n    od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 90 "Maple can also produce a graph showin
g this same data.  The 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([se
q([n, pop(n)], n = 1 .. 20)], \n        year = 1 .. 20, title = `Popul
ation`);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 72 "Now you can use these Maple tools to study the sequences \+
in this module." }}}}{MARK "0 2 1" 23 }{VIEWOPTS 1 1 0 1 1 1803 }