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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 61 "Sequences -- Pack Hunter
 Models -- Stretch Your Understanding" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 113 "The cell below illustrates the way i
n which Maple can be used to work with models like the ones in this mo
dule.  " }{TEXT 256 16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 359 "InitialValue := 100
:\nFcn := \n   proc(p)\n      if p < 500 then (1.5 * p/500) * p else (
2.0 - p/1000) * p fi\n   end:\n\npop :=\n   proc(n)\n      if n = 1 th
en InitialValue else Fcn(pop(n-1)) fi\n   end:\n\nfor k from 1 to 10\n
   do printf(`%4d %10.4f`, k, pop(k));\n      print();\n   od;\n\nplot
([seq([n, pop(n)], n = 1..10)],\n       year = 1.. 10, title = 'popula
tion');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 41 "The cell below defines the function  --  " }{TEXT 257 4 "
f(q)" }{TEXT -1 224 "  --  used in the marketing questions in this sec
tion.  The algebraic form of this function is not at all important.  I
n fact, usually functions like this one are determined from data and d
o not have a nice algebraic form.  " }{TEXT 258 90 "Evaluate the next \+
cell now and then use this function to answer the questions in the tex
t." }{TEXT -1 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "f :
= proc(q)\n       if q < 1000 then 500 * (1 - cos(Pi * q/1000)) else 1
000 fi\n     end:\n\nplot(\{'f(q)', q\}, q=0..2000, 0..2000, scaling=C
ONSTRAINED);\n" }}}}{MARK "0 0 0" 61 }{VIEWOPTS 1 1 0 1 1 1803 }