(*^

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                                Newton's Model of Cooling, Revisited

The cell below illustrates how the Mathematica  proced  NDSolve  can be used together with the Mathematica  Plot   procedure to study differential equations like Newton's Model of Cooling.  Evaluate it now and then use it as a model for studying the questions raised in this module.
;[s]
12:0,1;68,0;105,2;116,0;126,1;133,0;165,2;176,0;178,1;182,0;260,3;351,0;353,-1;
4:6,13,9,Times,0,12,0,0,0;3,13,9,Times,1,12,0,0,0;2,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[solution, Ambient, k, hight]

Ambient[t_] := Sin[t]

hight := 12.56
k := 1

solution =
NDSolve[{T'[t] == k * (Ambient[t] - T[t]),
         T[0] == 2}, T,
         {t, 0, hight}];
         
Plot[{T[t] /. solution, Ambient[t]},
     {t, 0, hight},
     PlotRange -> {-2, 2},
     PlotStyle -> {{RGBColor[0, 0, 1]},
                   {RGBColor[1, 0, 0]}}]
^*)