Concept explainers
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).
Trending nowThis is a popular solution!
Chapter 1 Solutions
Differential Equations
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage