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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 28 "Sequences -- Cobweb Diag
rams" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "T
he cell below defines a procedure  -- " }{TEXT 256 6 "cobweb" }{TEXT 
-1 89 "  -- that can be used to draw cobweb diagrams.\nThis procedure \+
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 " -- t
he 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 shown in th
e cobweb diagram \n\n" }{TEXT 260 27 "Evaluate the cell below now" }
{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     local blk
, rd, blu, frm, cobweblist, j;\n\n     cobweblist := \{line([first, 0]
, [first, fcn(first)])\}:\n\n     for j from 3 to n do\n        cobweb
list := 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([PopModel(fcn
, first, j-1), PopModel(fcn, first, j-1)],\n                  [PopMode
l(fcn, first, j-1), PopModel(fcn, first, j)])\}\n     od:\n\n     frm \+
:= display(\{line([0, 0], [0, top]),\n                     line([0, to
p], [top, top]),\n                     line([top, top], [top, 0]),\n  \+
                   line([top, 0], [0, 0])\},\n                     col
or = BLACK,\n                     axes = NONE,\n                     s
caling = CONSTRAINED):\n\n     blk := plot(f(p),\n                    \+
p = 0..top,\n                    y = 0..top,\n                    colo
r = BLACK,\n                    scaling = CONSTRAINED):\n\n     rd  :=
 display(cobweblist,\n                    color = RED,\n              \+
      axes = NONE,\n                    scaling = CONSTRAINED):\n\n   \+
  blu := display(\{line([0, 0], [top, top])\},\n                    co
lor = BLUE,\n                    axes = NONE,\n                    sca
ling = 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 al
ong 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 remem
ber;\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" 19 }{VIEWOPTS 1 1 0 1 1 1803 }