(*^

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                                      Newton's Law of Cooling

     The first cell below enters a list of equally spaced data points.  By cutting and pasting you can use your own data.  The same cell draws a graph of the data.  Notice the PlotRange option that specifies the range of the vertical axis.  Depending on the range of your data you may want to change this option.   Execute the cell below to see a graph of the data. 

;[s]
8:0,3;61,0;68,3;239,4;248,3;378,2;428,1;429,0;431,-1;
5:2,13,9,Times,0,12,0,0,0;1,13,9,Times,0,12,65535,0,0;1,13,9,Times,1,12,65535,0,0;3,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,65535;
:[font = input; preserveAspect; ]
Cooling := {
93.02,  90.23,  87.64,  85.57,  83.29,  81.45,  79.70,  78.03,                
76.69,  75.15,  73.91,  72.48,  71.10,  69.98,  68.90,  67.85,
66.62,  65.42,  64.45,  63.88,  62.95,  62.04,  61.14,  60.27,
59.75,  58.90,  58.23,  57.41,  56.92,  56.28,  55.33,  54.71,
54.10,  53.49,  52.75,  52.30,  51.87,  51.29,  50.71,  50.14,
49.72,  49.30,  48.75,  48.34,  47.93,  47.52,  46.98,  46.58,
46.05,  45.66,  45.26,  45.01,  44.62,  44.23,  43.85,  43.59,
43.21,  42.83,  42.45,  42.08,  41.83,  41.46,  41.21,  40.84,
40.60,  40.23,  39.86,  39.74,  39.38,  39.02,  38.90,  38.54,                
38.42,  38.06,  37.82,  37.59,  37.35,  37.11,  36.64,  36.52,                
36.29,  36.05,  35.94,  35.70,  35.47,  35.24,  35.01,  34.78,                
34.66,  34.31,  34.20,  33.97,  33.85,  33.62,  33.39,  33.16,                
32.93,  32.93,  32.82};

ListPlot[Cooling, 
         PlotRange -> {0, 100}, 
         PlotStyle -> RGBColor[1, 0, 0]]
;[s]
3:0,0;902,1;923,0;967,-1;
2:2,12,10,Courier,1,12,0,0,0;1,12,10,Courier,1,12,65535,0,65535;
:[font = special1; inactive; preserveAspect; ]
    
The next cell fits a curve of the form
     
                                      q[t] = A + k^(t-n) (q[n] - A)

to three equally spaced data points  Cooling[[n]], Cooling[[n + p]], and 
Cooling[[n + 2p]].  It then draws a graph showing the original data and the fitted curve.  Execute the cell below to see an example with a curve fitted to Cooling[[20]], Cooling[[40]], and Cooling[[60]].
;[s]
15:0,0;5,1;155,3;168,1;170,3;186,1;193,3;210,1;282,2;348,3;361,2;363,3;376,2;382,3;395,2;397,-1;
4:1,13,9,Times,0,12,0,0,0;4,13,9,Times,1,12,0,0,0;4,13,9,Times,1,12,65535,0,0;6,13,9,Times,1,12,0,0,65535;
:[font = input; preserveAspect; ]

n := 20;
p := 20;

A := (Cooling[[n + 2 p]] * Cooling[[n]] - Cooling[[n + p]]^2)/
     (Cooling[[n + 2 p]] - 2 * Cooling[[n + p]] + Cooling[[n]]);
     
k := ((A - Cooling[[n + p]])/(A - Cooling[[n]]))^(1/p);

Model[t_] := A + (k^(t - n)) * (Cooling[[n]] - A)

Show[ListPlot[Cooling,
     PlotStyle -> RGBColor[1,0,0],
     DisplayFunction -> Identity],
     ListPlot[Table[Model[j], {j, Length[Cooling]}],
     PlotStyle -> RGBColor[0,0,1],
     DisplayFunction -> Identity],
     PlotRange -> {0, 100},
     DisplayFunction -> $DisplayFunction]
^*)