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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 11 "Math 2280-2" }}{PARA 257 "" 0 "
" {TEXT -1 23 "Maple Project 1, Part 1" }}{PARA 259 "" 0 "" {TEXT 256 
23 "Investigation C page 88" }}{PARA 258 "" 0 "" {TEXT -1 17 "Solution
 Template" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
152 "(1)  Enter your Name and Student number in this space:  (You shou
ld know by now that you can mix computations with word processing in a
 Maple document.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 113 "(2)  Create a matrix whi
ch contains the world population data of Figure 2.1.9 on page 88.  Beg
in by initializing:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "rest
art:\n  #always a good idea when you start something new\nwith(linalg)
:\n   #so that you can do matrix operations" }}}{PARA 0 "" 0 "" {TEXT 
-1 75 "(You should start by using the menu to insert a Maple prompt in
 this area.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
260 "(3)  Create a collection of points which estimate ordered pairs o
f [P, (1/P)*(dP/dt)].  Use the centered difference approach discussed \+
in the text and the class handout.  Your populations will be those of \+
1965, 1970, ..., 1995; this will give you seven points." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 60 "(4)  Find the least squares line fit to the points in (3).  " }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 192 "(5)  Plot the least squares line which you fou
nd in (4), together with the points in (3).  You should obtain a figur
e analogous to Figure 2.1.8 on page 87.  You will need the plotting pa
ckage:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 234 "(6)  Using the \"a\" and \"b\" from your least squa
res line, and using the year 2000 population as P0, solve the logistic
 differential equation .  You may want to use \"dsolve\".  So you shou
ld probably load the differential equation tools:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools
):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 368 "(7)  Plo
t the world  populations vs. time which you obtained from Figure 2.1.9
, along with the solution to the logistic equation in (6), in one disp
lay.  If you did your work correctly the actual populations should be \+
close to those predicted by your solution (and this is no surprise sin
ce you used those populations to pick \"best\" parameters for the logi
stic curve)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 179 "(8)  The Population Division of the \+
United Nations predicts a world population of 8.177 billion people in \+
the year 2025.  What does your solution to the logistic equation predi
ct?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 110 "(9)  What is the human \"carrying capaci
ty\" of the earth currently, according to  your parameters \"a\" and \+
\"b\" ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 "END" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
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