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From: "Paul Hanson" <paul.hanson@mpi.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Flow problem
Date: Fri, 19 Nov 2010 19:30:22 +0000 (UTC)
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---
DUDE, I am so kicking myself for not taking this to the next level.  KUDOS.  
Paul
---
>   Instead of using discrete time intervals you can consider your equation as one in the infinitesimal, that is a differential equation.
> 
>  dv/dt = 10-.1*v
> 
> This is readily solved to be:
> 
>  v = 100-(100-v(0))*exp(-.1*t) = 100*(1+exp(-.1*t))
> 
>   Therefore, you can compute
> 
>  t = 0:180;
>  v = 100*(1+exp(-.1*t));
>  plot(t,v)
> 
>   Note: You will find that v drops down to essentially 100 very early in this period of time.  (I have assumed that the time units for dt in your original equation are also measured in minutes.)
> 
> Roger Stafford