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
t = time (independent variable),
r ( t ) = amount of particular radioactive isotope present at time t (dependent variable),
−λ = decay rate (parameter).
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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