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We model radioactive decay of an element or exponential increase of population using differential equations in Mathematica software.
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In[1]:= eqtn = r'@tD == -0.1 * r@tD;
gensol = DSolve@eqtn, r@tD, tD;
parsol = DSolve@8eqtn, r@0D � 200<, r@tD, tD;
greqtn = r@tD �. parsol;
Plot@Evaluate@greqtnD, 8t, 0, 20<, PlotLegends ® "Expressions",
PlotRange ® 80, 200<, PlotLabel ® "Decay Model", GridLines ® 883<, 8<<,
AxesLabel ® 8"Time", "Radioactive material in Grams"<Dgrval = greqtn �. t ® 3
Out[5]=
0 5 10 15 20
Time
50
100
150
200
Radioactive material in Grams
Decay Model
200. ã-0.1 t
Out[6]= 8148.164<
