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In Exercises 6—10, 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.
6. Model radioactive decay using the notation
t = time (independent variable),
r(t) = amount of particular radioactive isotope
present at time t (dependent variable),
−
Note that the minus sign is used so that
(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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Chapter 1 Solutions
Differential Equations
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell