{VERSION 3 0 "APPLE_PPC_MAC" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "8.Gabriel Johnson and Chri
s Deyton" }}{PARA 0 "" 0 "" {TEXT -1 487 "The problem we have is water
 flows into a lake from a creek and the water is comtaminated by spray
 from an orange grove.   The input and output was 300gal/min and the v
ol;ume of the lake was 100 million gallons(this is constant).   The co
ncentration changes from 35parts/1million gallons to 10parts/million g
allons and we are trying to find the time it takes for the concentrati
on to become less than 10parts /million gallons.  So we set up a de an
d used compartmental analysis to solve." }}{PARA 0 "" 0 "" {TEXT -1 
41 "We found our differential equation to be:" }}{PARA 0 "" 0 "" 
{TEXT -1 71 "dx/dt=(300g/min)(3.5*10^-5parts/gal) - (300g/min)(x(t)/10
0 million gal)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "x:=unapply(rhs(d
solve(\{diff(x(t),t)=(300*(3.5/10^5))-(300*(x(t)/100000000)),x(0)=35\}
,x(t))),t);                                                           \+
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGR6#%\"tG6\"6$%)operatorG%&ar
rowGF(,&$\"%+N\"\"!\"\"\"-%$expG6#,$9$#!\"$\"(+++\"$!%lMF/F(F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 179 "By using first order linear our x
(t) was exactly the same as maple came up with.  By the way our initia
l condition was when time=0 the concentration was 35 parts/1million ga
llons." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 189 "For the second part we divided x(t) by the total volume \+
of the lake, so that we are working in terms of concentration as we ar
e given originally in the problem.  Now we can nsolve for time." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "sol2:=x(t)/100000000;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol2G,&$\"+++++N!#9\"\"\"-%$expG6#,
$%\"tG#!\"$\"(+++\"$!++++lMF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "solve(sol2=1/10^5,t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+.I2)3\"!\"%" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 43 "We came up with the same solution as maple." }}}}
{MARK "0 0 0" 34 }{VIEWOPTS 1 1 0 1 1 1803 }