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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "p. 81 #5" }}{PARA 0 "" 0 "
" {TEXT -1 31 "Katie McDaniel and Jon Conowall" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 389 "This problem consists of a swimming pool with an in
itial volume of 10,000 gal and a chlorine concentation of 0.01%.  City
 water containing 0.001% chlorine enters the pool at 5 gal/min.  The s
olution of unknown chlorine concentration exits the pool at 5 gal/min.
  What is the percentage of chlorine in the pool after 1 hour?  How lo
ng until the chlorine concentration in the pool is 0.002%?" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "Initial condition
s x(0)=0.01%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 27 "inflow rate(gal of Cl/min):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "5*(.001/100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"+++++]!#9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "outflow rate(gal o
f Cl/min):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "5*(x(t)/10000
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%\"xG6#%\"tG#\"\"\"\"%+?" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "the differential equation is x'=in
flow rate-outflow rate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f
:=(diff(x(t),t)=.00005-(x(t)/2000));" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"fG/-%%diffG6$-%\"xG6#%\"tGF,,&$\"\"&!\"&\"\"\"F)#!\"\"\"%+?" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "the solution to the differential e
quation with the initial conditions:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "dsolve(\{f,x(0)=1\},x(t));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%\"xG6#%\"tG,&$\"+++++5!#5\"\"\"-%$expG6#,$F'#!\"\"\"
%+?$\"+++++!*F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "this is x(t) w
ith t=60min.  x is the gal of chlorine in 10000 gal of solution" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "evalf(.1000000000+.900000000
0*exp((-1/2000)*60));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-)4St*!#5
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "this is the percentage of the
 chlorine in the solution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "evalf((.9734009802/10000)*100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#$\"+-)4St*!#7" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "this is the gal
 of chlorine we will use in the second part of the problem." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf((.002/100)*10000);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++?!#5" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 64 "this is the total minutes to have .002% chlorine in the
 solution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "fsolve(.100000
0000+.9000000000*exp(-1/2000*t)=.2,t);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"+b\"\\WR%!\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "this th
e number of hours" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalf(
4394.449155/60);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+D>3Ct!\")" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "14 0 0" 74 }
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