In Exercise, we consider the phenomenon of radioactive decay which, from experimentation, we know behaves according to the law:
The rate at which a quantity of a radioactive isotope decays is proportional to the amount of the isotope present. The proportionality constant depends only on which radioactive isotope is used.
Model radioactive decay using the notation
Note that the minus sign is used so that λ > 0.
(a) Using this notation, write a model for the decay of a particular radioactive isotope.
(b) If the amount of the isotope present at t = 0 is r0, state the corresponding initial-value problem for the model in part (a).
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