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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 30 "Sequences -- Longterm Be
havior" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 
"The cell below defines a procedure  -- " }{TEXT 256 6 "cobweb" }
{TEXT -1 89 "  -- that can be used to draw cobweb diagrams.\nThis proc
edure requires three arguments.\n\n" }{TEXT 257 4 "fcn " }{TEXT -1 
100 " -- the function that describes how each term of the sequence is \+
computed from the preceding term.\n\n" }{TEXT 258 5 "first" }{TEXT -1 
50 " -- the value of the first term of the sequence.\n\n" }{TEXT 259 
1 "n" }{TEXT -1 76 " -- the number of terms of the sequence to be show
n in the cobweb diagram \n\n" }{TEXT 260 27 "Evaluate the cell below n
ow" }{TEXT -1 4 ".  \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1488 
"with(plots):\nwith(plottools):\n\nPopModel :=\n     proc(fcn, first, \+
n) \n        if n <= 1 then first else fcn(PopModel(fcn, first, n-1)) \+
fi:\n     end:\n\ncobweb := \n     proc(fcn, first, n, top)\n     loca
l blk, rd, blu, frm, cobweblist, j;\n\n     cobweblist := \{line([firs
t, 0], [first, fcn(first)])\}:\n\n     for j from 3 to n do\n        c
obweblist := cobweblist union\n            \{line([PopModel(fcn, first
, j-2), PopModel(fcn, first, j-1)],\n                  [PopModel(fcn, \+
first, j-1), PopModel(fcn, first, j-1)]), \n             line([PopMode
l(fcn, first, j-1), PopModel(fcn, first, j-1)],\n                  [Po
pModel(fcn, first, j-1), PopModel(fcn, first, j)])\}\n     od:\n\n    \+
 frm := display(\{line([0, 0], [0, top]),\n                     line([
0, top], [top, top]),\n                     line([top, top], [top, 0])
,\n                     line([top, 0], [0, 0])\},\n                   \+
  color = BLACK,\n                     axes = NONE,\n                 \+
    scaling = CONSTRAINED):\n\n     blk := plot(f(p),\n               \+
     p = 0..top,\n                    y = 0..top,\n                   \+
 color = BLACK,\n                    scaling = CONSTRAINED):\n\n     r
d  := display(cobweblist,\n                    color = RED,\n         \+
           axes = NONE,\n                    scaling = CONSTRAINED):\n
\n     blu := display(\{line([0, 0], [top, top])\},\n                 \+
   color = BLUE,\n                    axes = NONE,\n                  \+
  scaling = CONSTRAINED):\n\n     display([blk, rd, blu, frm]);   \n  \+
end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 133 "The following cell illustrates how this new procedure can used
 along with other Maple procedures to investigate long term behavior. \+
 " }{TEXT 261 16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 337 " f := p -> 4.0 * (1 - .001
 * p) * p:\n  cobweb(f, 50, 30, 1000);\n\n  pop := proc(n) option reme
mber;\n         if n = 1 then 50 else f(pop(n-1)) fi\n         end:\n
\n  for k from 1 to 30 \n      do printf(`%4d %10.4f`, k, pop(k));\n  \+
    print();\n      od;\n\n  plot([seq([n, pop(n)], n = 1 .. 30)], \n \+
       year = 1 .. 30, title = `Population`);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 30 }{VIEWOPTS 1 1 0 1 1 1803 
}