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?
>
>
>
> 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
>

```

• Prev by Date: Re: Self-teaching snag
• Next by Date: Re: Self-teaching snag
• Previous by thread: Re: Self-teaching snag
• Next by thread: Re: Self-teaching snag