question

*To*: mathgroup at smc.vnet.net*Subject*: [mg9245] question*From*: "Roeland J. Steenhuis" <pcsteenh at worldonline.nl>*Date*: Fri, 24 Oct 1997 01:00:59 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I'm a first year Chemistry student at the University of Groningen, The Netherlands. I have a problem. I don't know if this is the place to be for questions, but i'll ask anyway. The professor gave us a Mathematica-problem to solve, but i just can't figure it out! Maybe you can help. The problem is: ------------------- You are sober at t=t1 and you drink a beer. We assume that the amount of alcohol in your blood, y, will rise instantly from 0 to one unit: y[t1]=1 If you don't drink anymore, the amount of alcohol in your blood will drop back to zero, in accordance with to this differential equation: y'[t] = (-a*y)/(b+y) (1) where a and b are positive constants, dependent on body-properties. Let's say a=1/10 and b=1/2. A dutch saying is: 'You can't walk on one leg', so you take another beer at t=t2, a third beer at t=t3 , a fourth at t=t4 and one at t=t5. After every beer the amount of alcohol in your blood decreases according to equation(1). You have 60 minutes time to drink five beers, 0</=t1</=t2</=t3</=t4</=t5</=60 (</=, smaller or the same as). At which times you need to drink your beers to keep the maximum amount of alcohol in your blood as low as possible (for 0 </= t </= 60)? ---------------------------------------------- I had to translate it from Dutch into English, so i hope you understand it. I found out a few things (before i tried to use Mathematica): - You take a beer at t1=0 and t5=60 - The last four maximums (at t2,t3,t4 and t5) have the same y - value (i don't if i'm right here, pls correct me if i'm wrong) As you see it's not much. It got even worse when i tried to use Mathematica! All i get are errors! Please help me.. Roeland J. Steenhuis pcsteenh at worldonline.nl

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