exponential decay model in differential equations

1
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"<D grval = greqtn .t 3 Out[5]= 0 5 10 15 20 Time 50 100 150 200 Radioactive material in Grams Decay Model 200. ª -0.1 t Out[6]= 8148.164<

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DESCRIPTION

We model radioactive decay of an element or exponential increase of population using differential equations in Mathematica software.

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Page 1: Exponential Decay Model in Differential Equations

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<