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MathGroup Archive 2007

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Re: Self-teaching snag

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74601] Re: [mg74556] Self-teaching snag
  • From: leigh pascoe <leigh at cephb.fr>
  • Date: Tue, 27 Mar 2007 04:10:37 -0500 (EST)
  • References: <200703260704.CAA11373@smc.vnet.net>

Todd Allen wrote:
> Hi All,
>
>    I am trying to refresh my skills in basic problem
> solving using Mathematica, but am running into some
> difficulties which are beginning to make me suspicious
> of Mathematica itself.  (I probably should be
> suspicious of my own brain...but you know how that is
> :-)
>
> Here is the scenario:  I have written a basic function
> to tell me what percentage of battery power will
> remain in a battery after x number of days, provided
> that we start with a full charge and lose 5% of that
> charge per day.
>
> If you execute the following code in Mathematica
> (V5.1):
>
> charge[0]=1.0 (* 100% *);
> charge[day_]:=(charge[day-1]-(0.05*charge[day-1]));
> charge[20]
>
> I receive an output of 0.358486 for my query at the 20
> day mark.....so, no problem so far.
>
> However, when I try to ask for the output at
> charge[35], mathematica seems to enter an endless
> calculation.  I've let the computer run for as long as
> 5 minutes without getting an answer.  Is there
> something wrong with my function, my version of
> Mathematica or something else I haven't considered?
>
>
> Additionally,
>
> When I try the following:
>
> In[145]:=
> Solve[charge[day]==0.15,day];
>
> Mathematica gives me the error:
> "$RecursionLimit::reclim: Recursion depth of 256
> exceeded."
>
> I am trying to ask Mathematica to tell my how many
> days it takes to reduce the battery power to 15
> percent, but I must be messing something up??
>
> If anyone has any pointers, I'd certainly appreciate
> it, because I am a little stuck right now.
>
> Best regards,
> Todd Allen
>
>
>  
> ____________________________________________________________________________________
> We won't tell. Get more on shows you hate to love 
> (and love to hate): Yahoo! TV's Guilty Pleasures list.
> http://tv.yahoo.com/collections/265 
>
>
>
>
>   
This is not exactly an answer to your question, but recursive 
definitions are notoriously inefficient. However your basic problem is 
that you are mixing a function that is defined for integers and trying 
to solve an equation whose solution is not an exact multiple of days. 
Similarly when you try to find charge[30] you are probably suffering 
from rounding errors due to machine precision and never arriving at the 
root of your recursion (charge[0]). For example if you try to evaluate 
charge[30.00000000000000001] Ma will never arrive at a value by the 
recursive search.

Your problem is easily soluble if you formulate it directly as a 
continuous variable as follows.

charge[x]:=.95^x;
charge[30]
for the first part,

or

Solve[ch[x]\[Equal].15,x]

for the second.

with a pencil and paper x=Log[.15]/Log[.95]=36.9857, which is the answer 
returned by Solve.

I hope this helps.

Leigh



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