Re: Self-teaching snag

*To*: mathgroup at smc.vnet.net*Subject*: [mg74580] Re: Self-teaching snag*From*: "Szabolcs" <szhorvat at gmail.com>*Date*: Tue, 27 Mar 2007 03:59:16 -0500 (EST)*References*: <eu7re0$b6p$1@smc.vnet.net>

On Mar 26, 9:06 am, 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. Here Mathematica evaluates the two charge[day-1] *before* evaluating Plus (i.e. adding them). There are two charge[ ] expressions, so with every recursion step, the number of evaluations is doubled. For day==35 you get 2^35 == 34359738368 a very large number of evaluations (which takes a very long time). If you use charge[day_] := 0.95 charge[day-1], the computation will be much faster. > 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." Here Mathematica tries to evaluate charge[day], but day is a symbol (not a number), so it never reaches 0, and the evaluation will never end. (It will go down as day, day-1, day-2 etc.) > > 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?? Your definition of the charge[ ] function works only for integer numbers (for a non-integer day value, you will never get 0, no matter how many times you subtract 1). So there might not even be an integer 'day' number that gives you a charge of 0.15. You can check this by looking at all some charge[day] values for small 'day' values. In[22]:= Table[charge[n],{n,1,50}] Out[22]= {0.95,0.9025,0.857375,0.814506,0.773781,0.735092,0.698337,0.66342,0.630249,0.\ 598737,0.5688,0.54036,0.513342,0.487675,0.463291,0.440127,0.41812,0.397214,0.\ 377354,0.358486,0.340562,0.323534,0.307357,0.291989,0.27739,0.26352,0.250344,\ 0.237827,0.225936,0.214639,0.203907,0.193711,0.184026,0.174825,0.166083,0.\ 157779,0.14989,0.142396,0.135276,0.128512,0.122087,0.115982,0.110183,0.104674,\ 0.0994403,0.0944682,0.0897448,0.0852576,0.0809947,0.076945} You may want to look at RSolve if you want to get a closed expression for your charge[] function using Mathematica. But this problem is best described by a differential equation (if you want to work with a continuous day variable, that is)