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MathGroup Archive 1997

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  • 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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