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{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "Dissolution Models" }}
{PARA 0 "" 0 "" {TEXT 275 5 "First" }{TEXT -1 103 " visit the CKM Inte
rnet text and view the kinetigram definition for Makoid-Banakar Dissol
ution Models. " }}{PARA 0 "" 0 "" {TEXT 278 4 "Then" }{TEXT -1 89 " cl
ick through the following example, Example 1, to see how to use this i
nteractive text." }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 45 " Makoid-Banak
ar Dissolution Models: Example 1" }}{PARA 0 "" 0 "" {TEXT -1 429 "Supp
ose we have 120 mg of a drug for which we would like total dissolution
 in 2 hours. We will use the following type of Makoid-Banakar function
, as defined in the CKM Internet text, to model the dissolution proces
s. We will create several different models by using different values o
f n, i.e. n = 1, 2, 3, 1/2, 1/3, 3/2, 4/3. Below n is set to 1. See wh
at this model looks like by working your way through the interactive t
ext. " }{TEXT 257 45 "Just click into a red area and press <Enter>." }
{TEXT -1 130 " When you finish come back up here and set n to 2, and t
hen work your way through the red areas again. Repeat for each value o
f n." }}{PARA 0 "" 0 "" {TEXT 256 48 "Start Here:  Enter the value of \+
n and your name." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 
0 139 "restart:n:=1:\nName:=`John Pais`:\nDigits:=7:\nntxt:=convert(n,
string):\nf:=t->t^n:\ndrug_d:=unapply(c*f(t)*exp(-k*t),t):\n'drug_d(t)
'=drug_d(t);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 258 4 "Next" }
{TEXT -1 157 ", we find the derivative of drug_d(t) (which D-Rules do \+
you need here?), and a formula for t_peak by setting this derivative e
qual to zero and solving for t." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }{MPLTEXT 1 0 156 "tsf:=t->D(drug_d)(t):\n'D'(drug_d(t))=D(drug_d)(t
);\nfactor(tsf(t))=0;\nt_peak1:=`minus`(\{solve(tsf(t)=0,t)\},\{0\}):
\nt_peak2:=op(1,t_peak1):\n't_peak' = t_peak2;\n" }}}{PARA 0 "" 0 "" 
{TEXT 259 5 "Enter" }{TEXT -1 76 " the value of t_peak given by the in
itial data of the model and determine k:" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 86 "t_peak:=2:\nk1:=solve(t_peak2=t_peak,k
):\n't_peak'=t_peak,\nt_peak2=t_peak,\n'k'=eval(k1);" }}}{PARA 0 "" 0 
"" {TEXT 260 5 "View " }{TEXT -1 95 "our Makoid-Banakar function so fa
r, by substituting this value of k into our original function:" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 52 "drug_d:=t->c*f(
t)*exp(-k1*t):\n'drug_d(t)'=drug_d(t);" }}}{PARA 0 "" 0 "" {TEXT 261 
5 "Enter" }{TEXT -1 78 " the value of the dose given by the initial da
ta of the model and determine c:" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 
"" }{MPLTEXT 1 0 218 "dose:=120:\ndrug_d:=t->c*f(t)*exp(-k1*t):\n't_pe
ak'=t_peak,'dose'=dose;\n'drug_d(t_peak)=dose';\ndrug_d('t')=dose;\ndr
ug_d(t_peak)=dose;\nc0:=fsolve(drug_d(t_peak)=dose,c):\nc1:=evalf(roun
d(100*c0)/100,ilog10(c0)+3):\n'c'=c1;\n" }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }{TEXT 256 5 "View " }{TEXT -1 98 "our final Makoid-Banakar funct
ion by substituting this value of c into our previous version above:" 
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 525 "drug_d:=t->c
1*f(t)*exp(-k1*t):\n'drug_d(t)'=drug_d(t);\np1:=plot(drug_d(t),t=0..t_
peak,0..dose,color=blue):\np2:=plot([[0,dose],[t_peak,dose]],linestyle
=3,color=red):\np3:=plot([[t_peak,0],[t_peak,dose]],linestyle=3,color=
red):\ndissolution_plot:=plots[display](\n                   [p1,p2,p3
],\n                    labels=[`                 t (hours)`,`(mg) `],
\n                    titlefont=[HELVETICA,DEFAULT,14],\n             \+
     title=`   `||Name||`'s Dissolution Model:  n = `||ntxt):\ndissolu
tion_plot;\n'drug_d(t)'=drug_d(t):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 48 "Check Combi
ned Plot of Drug Dissolution Profiles" }}{PARA 0 "" 0 "" {TEXT -1 90 "
Using the interactive text below you may check your answers to part (c
) on exercises like " }{TEXT 262 13 "DM Exercise 3" }{TEXT -1 5 " and \+
" }{TEXT 263 13 "DM Exercise 4" }{TEXT -1 33 ". The example below is s
etup for " }{TEXT 264 13 "DM Exercise 3" }{TEXT -1 1 " " }{TEXT 265 3 
"(c)" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT 266 5 "Enter" }{TEXT 
-1 16 " the values for " }{TEXT 267 4 "dose" }{TEXT -1 2 ", " }{TEXT 
268 6 "t_peak" }{TEXT -1 2 ", " }{TEXT 269 9 "t_percent" }{TEXT -1 54 
", and the correct defining expressions (formulas) for " }{TEXT 270 7 
"drug_d1" }{TEXT -1 2 ", " }{TEXT 271 7 "drug_d2" }{TEXT -1 2 ", " }
{TEXT 272 7 "drug_d3" }{TEXT -1 6 ", and " }{TEXT 273 7 "drug_d4" }
{TEXT -1 41 ", in order to check a different exercise." }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 2986 "Digits:=7:\ndose:=40
0:\nt_peak:=8:\nt_percent:=2:\ndrug_d1:=t->305.39*t^(1/4)*exp(-(1/32)*
t):\ndrug_d2:=t->178.03*t^(3/4)*exp(-(3/32)*t):\ndrug_d3:=t->94.84*t^(
4/3)*exp(-(1/6)*t):\ndrug_d4:=t->5.33*t^4*exp(-(1/2)*t):\ndelta:=0.05*
dose:\nt0:=t_percent:\nstr_t0:=convert(t0,string):\nd_d1:=evalf(round(
100*evalf(drug_d1(t0)))/100,\n            ilog10(evalf(drug_d1(t0)))+3
):\nd_d2:=evalf(round(100*evalf(drug_d2(t0)))/100,\n            ilog10
(evalf(drug_d2(t0)))+3):\nd_d3:=evalf(round(100*evalf(drug_d3(t0)))/10
0,\n            ilog10(evalf(drug_d3(t0)))+3):\nd_d4:=evalf(round(100*
evalf(drug_d4(t0)))/100,\n            ilog10(evalf(drug_d4(t0)))+3):\n
pd_d1:=evalf(trunc(round(10000*evalf(drug_d1(t0)/dose)))/100,4):\npd_d
2:=evalf(trunc(round(10000*evalf(drug_d2(t0)/dose)))/100,4):\npd_d3:=e
valf(trunc(round(10000*evalf(drug_d3(t0)/dose)))/100,4):\npd_d4:=evalf
(trunc(round(10000*evalf(drug_d4(t0)/dose)))/100,4):\nstr_pd_d1:=conve
rt(pd_d1,string):\nstr_pd_d2:=convert(pd_d2,string):\nstr_pd_d3:=conve
rt(pd_d3,string):\nstr_pd_d4:=convert(pd_d4,string):\ndd1_txt:=` drug_
d1: `||str_pd_d1||` %`:\ndd2_txt:=` drug_d2: `||str_pd_d2||` %`:\ndd3_
txt:=` drug_d3: `||str_pd_d3||` %`:\ndd4_txt:=` drug_d4: `||str_pd_d4|
|` %`:\np[0]:=plot(drug_d1(t),t=0..t_peak,0..dose,color=blue):\np[1]:=
plot(drug_d2(t),t=0..t_peak,0..dose,color=blue):\np[2]:=plot(drug_d3(t
),t=0..t_peak,0..dose,color=blue):\np[3]:=plot(drug_d4(t),t=0..t_peak,
0..dose,color=blue):\np[4]:=plots[textplot]([0,drug_d1(t0)+delta, dd1_
txt],\n            font=[HELVETICA,DEFAULT,11],color=black,align=RIGHT
):\np[5]:=plot([[0,drug_d1(t0)],[t0,drug_d1(t0)]],\n             lines
tyle=3,color=black):\np[6]:=plots[textplot]([0,drug_d2(t0)+delta, dd2_
txt],\n            font=[HELVETICA,DEFAULT,11],color=black,align=RIGHT
):\np[7]:=plot([[0,drug_d2(t0)],[t0,drug_d2(t0)]],\n             lines
tyle=3,color=black):\np[8]:=plots[textplot]([0,drug_d3(t0)+delta, dd3_
txt],\n            font=[HELVETICA,DEFAULT,11],color=black,align=RIGHT
):\np[9]:=plot([[0,drug_d3(t0)],[t0,drug_d3(t0)]],\n             lines
tyle=3,color=black):\np[10]:=plots[textplot]([0,drug_d4(t0)+delta, dd4
_txt],\n            font=[HELVETICA,DEFAULT,11],color=black,align=RIGH
T):\np[11]:=plot([[0,drug_d4(t0)],[t0,drug_d4(t0)]],\n              li
nestyle=3,color=black):\np[12]:=plot([[t0,0],[t0,drug_d1(t0)]],linesty
le=3,color=black):\np[13]:=plot([[0,dose],[t_peak,dose]],linestyle=3,c
olor=red):\np[14]:=plot([[t_peak,0],[t_peak,dose]],linestyle=3,color=r
ed):\ndissolution_plot:=plots[display]([seq(p[j],j=0..14)],  \n       \+
         labels=[`t (hours)`,`(mg) `],\n                titlefont=[HEL
VETICA,BOLD,12],\n      title=`          Combined Plot of Drug Dissolu
tion Profiles`):\n'drug_d1(t)'=drug_d1(t),\n'drug_d2(t)'=drug_d2(t);\n
'drug_d3(t)'=drug_d3(t),\n'drug_d4(t)'=drug_d4(t);\ndissolution_plot;
\n` drug_d1 after `||str_t0||` hrs`=d_d1*`mg `,pd_d1*`% `;\n` drug_d2 \+
after `||str_t0||` hrs`=d_d2*`mg `,pd_d2*`% `;\n` drug_d3 after `||str
_t0||` hrs`=d_d3*`mg `,pd_d3*`% `;\n` drug_d4 after `||str_t0||` hrs`=
d_d4*`mg `,pd_d4*`% `;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 0 "" }{TEXT 274 60 "Formula for
 the First Derivative of drug_d(t) and for t_peak" }{TEXT -1 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"DG6#*(%\"cG\"\"\")%\"tG%\"nGF)-%$
expG6#,$*&%\"kGF)F+F)!\"\"F),&*&-F%6#*&F(F)F*F)F)F-F)F)*(-F%6#F-F)F(F)
F*F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%.~~~~~~~~~~~~~G,&**%#~nG\"
\"\"%\"cGF()%\"tG,&%\"nGF(!\"\"F(F(-%$expG6#,$*&%\"kGF(F+F(F.F(F(**F/F
(F4F(%#~cGF()F+F-F(F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G**%\"cG\"
\"\")%\"tG,&%\"nGF'!\"\"F'F'-%$expG6#,$*&%\"kGF'F)F'F,F',&F+F'F1F,F'" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#%]oSo,~we~have~the~following~formula
~for~the~derivative~of~drug_d(t):G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/-%\"DG6#*(%\"cG\"\"\")%\"tG%\"nGF)-%$expG6#,$*&%\"kGF)F+F)!\"\"F)**F(
F))F+,&F,F)F3F)F)F-F),&F,F)F1F3F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
UWhich~we~can~use~to~find~t_peak~in~terms~of~n~and~k:G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/**%\"cG\"\"\")%\"tG,&%\"nGF&!\"\"F&F&-%$expG6#,$*
&%\"kGF&F(F&F+F&,&F*F&F0F+F&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
%'t_peakG*&%\"nG\"\"\"%\"kG!\"\"" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 
0 "" }{TEXT 276 65 "Formula for the Second Derivative of drug_d(t) and
 for t_max_rate" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-*$)%\"DG\"\"#\"\"
\"6#*(%\"cGF))%\"tG%\"nGF)-%$expG6#,$*&%\"kGF)F.F)!\"\"F)-F'6#-F'F*" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G-%\"DG6#**%\"cG\"\"\")%\"tG,&%\"n
GF*!\"\"F*F*-%$expG6#,$*&%\"kGF*F,F*F/F*,&F.F*F4F/F*" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/%!G,&*&-%\"DG6#*(%\"cG\"\"\")%\"tG,&%\"nGF,!\"\"F,F
,-%$expG6#,$*&%\"kGF,F.F,F1F,F,,&F0F,F6F1F,F,**-F(6#F8F,F+F,F-F,F2F,F,
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G,&*,%\"cG\"\"\")%\"tG,&%\"nGF(
!\"#F(F(-%$expG6#,$*&%\"kGF(F*F(!\"\"F(,(F,F(F4F(F2F4F(,&F,F(F2F4F(F(*
*F3F(F'F()F*,&F,F(F4F(F(F.F(F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G
**%\"cG\"\"\")%\"tG,&%\"nGF'!\"#F'F'-%$expG6#,$*&%\"kGF'F)F'!\"\"F',**
$)F+\"\"#F'F'F+F3*(F+F'F2F'F)F'F,*&)F2F7F')F)F7F'F'F'" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%aoSo,~we~have~the~following~formula~for~the~2nd~d
erivative~of~drug_d(t):G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-*$)%\"DG
\"\"#\"\"\"6#*(%\"cGF))%\"tG%\"nGF)-%$expG6#,$*&%\"kGF)F.F)!\"\"F)**F,
F))F.,&F/F)!\"#F)F)F0F),**$)F/F(F)F)F/F6*(F/F)F5F)F.F)F:*&)F5F(F))F.F(
F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%`oWhich~we~can~use,~when~n~
>~1,~to~find~t_max_rate~in~terms~of~n~and~k:G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/**%\"cG\"\"\")%\"tG,&%\"nGF&!\"#F&F&-%$expG6#,$*&%\"kG
F&F(F&!\"\"F&,**$)F*\"\"#F&F&F*F2*(F*F&F1F&F(F&F+*&)F1F6F&)F(F6F&F&F&
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%+t_max_rateG*&,&%\"nG\"\"\"
*$-%%sqrtG6#F'F(!\"\"F(%\"kGF-" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 0 
"" }{TEXT 277 72 "Formula for tif(t),  the First Derivative of tif(t),
 and t_min_intercept" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/-%\"fG6#%\"tG*(%\"cG\"\"\")F'%\"nGF*-%$expG6#,$*&%\"kGF*F'F*!\"\"F*
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%[oFrom~our~formula~(above)~for~th
e~derivative~of~drug_d(t)~=~f(t):G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/-%$tsfG6#%\"tG**%\"cG\"\"\")F',&%\"nGF*!\"\"F*F*-%$expG6#,$*&%\"kGF*F
'F*F.F*,&F-F*F3F.F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%boNow,~use~the
~defining~relationship~between~tsf(t)~and~tif(t)~to~obtain:G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%$tifG6#%\"tG**%\"cG\"\"\")F'%\"nGF*-%$exp
G6#,$*&%\"kGF*F'F*!\"\"F*,(F*F*F,F3F1F*F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%\\oNext,~(like~our~work~above)~we~may~find~the~derivat
ive~of~tif(t):G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DtifG6#%\"tG,$*
*%\"cG\"\"\")F',&%\"nGF+!\"\"F+F+-%$expG6#,$*&%\"kGF+F'F+F/F+,**$)F.\"
\"#F+F+F.F/*(F.F+F5F+F'F+!\"#*&)F5F9F+)F'F9F+F+F+F/" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%eoWhich~we~can~use,~when~n~>~1,~to~find~t_min_interc
ept~in~terms~of~n~and~k:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%0t_min_
interceptG*&,&%\"nG\"\"\"*$-%%sqrtG6#F'F(!\"\"F(%\"kGF-" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%eoWhy~is~the~formula~for~t_min_intercept~the~sa
me~as~for~t_max_rate~(above)?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%WCa
n~you~clearly~explain~exactly~what~is~going~on~here?G" }}}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 49 "Check t_max_rate and the Maximum Dissolut
ion Rate" }}{PARA 0 "" 0 "" {TEXT -1 78 "Using the interactive text be
low you may check your answers to exercises like " }{TEXT 279 17 "DM E
xercise 3 (d)" }{TEXT -1 52 ", and the example below is setup for this
 exercise. " }{TEXT 287 4 "NOTE" }{TEXT -1 88 " that if n < 1 then our
 formula for t_max_rate doesn't work (why?) and will generate an " }
{TEXT 288 13 "error message" }{TEXT -1 7 " below." }}{PARA 0 "" 0 "" 
{TEXT 280 5 "Enter" }{TEXT -1 16 " the values for " }{TEXT 281 4 "dose
" }{TEXT -1 2 ", " }{TEXT 282 6 "t_peak" }{TEXT -1 2 ", " }{TEXT 283 
1 "c" }{TEXT -1 2 ", " }{TEXT 284 1 "n" }{TEXT -1 6 ", and " }{TEXT 
285 1 "k" }{TEXT -1 41 ", in order to check a different exercise." }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "
" }{MPLTEXT 1 0 572 "restart:Digits:=7:\ndose:=400:\nt_peak:=8:\nc:=94
.84:\nn:=4/3:\nk:=1/6:\nntxt:=convert(n,string):\nktxt:=convert(k,stri
ng):\nctxt:=convert(c,string):\nf:=t->c*t^n*exp(-k*t):\nt_max_rate:=(n
,k)->((n-sqrt(n))/k):\ntsf:=t->c*t^(n-1)*exp(-k*t)*(n-k*t):\ntif:=t->c
*t^n*exp(-k*t)*(1-n+k*t):\nDtsf:=t->c*t^(n-2)*exp(-k*t)*(n^2-n-2*n*k*t
+k^2*t^2):\nDtif:=t->-c*t^(n-1)*exp(-k*t)*(n^2-n-2*n*k*t+k^2*t^2):\n`F
ormulas for your Makoid-Banakar Dissolution Model`,\n`drug_d(t) = f(t)
:`;\n'f(t)'=f(t),'t_max_rate'=t_max_rate('n','k');\n'tsf(t)'=tsf(t),'t
if(t)'=tif(t);\n'Dtsf(t)'=Dtsf(t),'Dtif(t)'=Dtif(t);" }}}{PARA 0 "" 0 
"" {TEXT -1 0 "" }{TEXT 286 4 "Next" }{TEXT -1 109 " create the plot o
f the dissolution profile for the model, including t_max_rate and the \+
max dissolution rate." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }{MPLTEXT 1 0 1628 "delta:=.05*dose:
\nt_maxrate:=t_max_rate(n,k):\nbot:=evalf(tif(t_maxrate) - delta):\nt_
maxrate_txt:=convert(evalf(t_maxrate,4),string):\ndrate_txt:=convert(e
valf(tsf(t_maxrate),4),string):\nrp[1]:=plot(f(t),t=0..t_peak,bot..dos
e,\n    labels=[`                                        t (hours)`,`(
mg) `],\n    color=blue):\nrp[2]:=plot(tif(t),t=0..t_peak,bot..dose,\n
    labels=[`                                        t (hours)`,`(mg) \+
`],\n    color=magenta):\nrp[3]:=plot([[t_maxrate,f(t_maxrate)],[t_max
rate,tif(t_maxrate)]],\n              linestyle=1,color=red):\nrp[4]:=
plot([[0,tif(t_maxrate)],[t_maxrate,f(t_maxrate)]],\n              lin
estyle=1,color=red):\nrp[5]:=plot([[0,tif(t_maxrate)],[t_maxrate,tif(t
_maxrate)]],\n              linestyle=1,color=red):\nrp[6]:=plot([[0,d
ose],[t_peak,dose]],linestyle=3,color=red):\nrp[7]:=plot([[t_peak,0],[
t_peak,dose]],linestyle=3,color=red):\nrp[8]:=plots[textplot](\n      \+
    [0,dose-delta,` max dissolution rate = `||drate_txt||` mg/hr`],\n \+
             font=[HELVETICA,DEFAULT,11],\n              color=red,ali
gn=RIGHT):\nrp[9]:=plots[textplot](\n      [0,dose-3*delta,`          \+
     t_max_rate = `||t_maxrate_txt||` hrs`],\n              font=[HELV
ETICA,DEFAULT,11],\n              color=red,align=RIGHT):\nplots[displ
ay]([seq(rp[j],j=1..9)],\n                titlefont=[HELVETICA,BOLD,12
],\ntitle=`          Dissolution Model:  c = `||ctxt||`, n = `||ntxt||
`, k = `||ktxt);\n\n'`Let f(t) = drug_d(t) and solve:  f ''`(t)'=0;\n'
t_max_rate'=t_max_rate('n','k');\ntmr:=evalf(t_max_rate(n,k)):\n't_max
_rate'=evalf(t_max_rate(n,k))*hrs;\n'`f '`(t)'=tsf(t);\n'`f '`'(tmr)=e
valf(tsf(t_max_rate(n,k)))*'mg/hr';\n\n\n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}}}{MARK "0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }