Re: Self-teaching snag
- To: mathgroup at smc.vnet.net
- Subject: [mg74597] Re: [mg74556] Self-teaching snag
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Tue, 27 Mar 2007 04:08:26 -0500 (EST)
- Reply-to: hanlonr at cox.net
To speed recursions up, add memory to the function definition so that it doesn't repeat prior recursions.
Clear[charge1];
charge1[0]=1;
charge1[day_Integer?Positive]:=
charge1[day]=0.95charge1[day-1];
charge1[20]
0.358486
charge1[35]
0.166083
However, the recursion can be avoided with
Clear[charge2,rate];
charge2[day_,rate_:0.95]:=rate^day;
Off[Solve::ifun];
d=day/.Solve[charge2[day]==0.15,day][[1]]
36.9857
Plot[charge2[day],{day,0,40},
Epilog->{Red, AbsolutePointSize[4],
Point/@Table[{n,charge1[n]},{n,0,40,4}],
Blue,AbsoluteDashing[{5, 10}],
Line[{{0,0.15},{d,0.15},{d,0}}]},
ImageSize->500];
If the result for charge2 is not obvious it can be obtained from RSolve
Clear[charge,day,rate];
charge[day]/.RSolve[{charge[day]==rate*
charge[day-1],charge[0]==1},charge[day],day][[1]]
rate^day
Bob Hanlon
---- Todd Allen <genesplicer28 at yahoo.com> 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
>
>
>
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