RE: Parametric plot

*To*: mathgroup at smc.vnet.net*Subject*: [mg49222] RE: [mg49195] Parametric plot*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 8 Jul 2004 02:50:57 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Danilo, How about this... data = {Km -> 10, Vmax -> 15}; Clear[t]; eqn = (s0/Km)*x - Log[1 - x] == (Vmax/Km)*t; Solve[eqn, t][[1,1]]; t[s0_][x_] = t /. % /. data; (1/15)*(s0*x - 10*Log[1 - x]) Needs["Graphics`Colors`"] ParametricPlot[Evaluate[MapThread[{t[#1][x], x} & , {{1, 20, 100}}]], {x, 0, 1}, Epilog -> {Text[Vmax == (Vmax /. data), {12, 0.8}, {-1, 0}], Text[Km == (Km /. data), {12, 0.7}, {-1, 0}], Text[StyleForm[1, Background -> Linen], {t[1][0.8], 0.8}], Text[StyleForm[20, Background -> Linen], {t[20][0.7], 0.7}], Text[StyleForm[100, Background -> Linen], {t[100][0.5], 0.5}]}, Frame -> True, FrameLabel -> {t, x}, PlotLabel -> SequenceForm[ "Batch Kinetics for Various ", Subscript[S, 0]], Background -> Linen, ImageSize -> 450]; I used MapThread to build a table of parametrizations for the various S0's. I used Epilog to add text labeling to the plot and to the three curves. Many years ago when I was working as a programmer for a biochemist my wife turned to me one evening and asked: "Was Einstein a biochemist?" This left me completely confused but it was all cleared up several days later when she received the following communication from The Relativity Institute. Dear Ms. Park, Never have we been so smitten to be confused with Michaelis-Menten. This grevious error as tried us sorely. Signed, Yours Truly, Michelson-Morley But now it seems that Bianchi is also a biochemist! David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Danilo Bianchi [mailto:kaiowaa at bol.com.br] To: mathgroup at smc.vnet.net A str batch reactor model following Michaelis-Menten kinetics gives the function: (S0\Km)x - Log[1 - x] = (Vmax\Km) t where x is the proportion of substrate converted, S0 is, say, 1, 20 and 100 g/L, Km is 10 and Vmax is 15. How to plot the curves (in the same graphic) for x varying from zero to 1 against t (from zero to 15, with the given values?