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6. 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 > > 0. (a) Using this notation, write a model for the decay of a particular radioactive iso- tope. = (b) If the amount of the isotope present at t initial-value problem for the model in part (a). 0 is ro, state the corresponding

6. 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 > > 0. (a) Using this notation, write a model for the decay of a particular radioactive iso- tope. = (b) If the amount of the isotope present at t initial-value problem for the model in part (a). 0 is ro, state the corresponding

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Exercises 6-10, we consider the phenomenon of radioactive decay which, from ex- perimentation, 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), = amount of particular radioactive isotope present at time t (dependent variable), -λ = decay rate (parameter). r(t) Note that the minus sign is used so that > > 0. (a) Using this notation, write a model for the decay of a particular radioactive iso- tope. (b) If the amount of the isotope present at t = 0 is ro, state the corresponding initial-value problem for the model in part (a).
Transcribed Image Text:In Exercises 6-10, we consider the phenomenon of radioactive decay which, from ex- perimentation, 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), = amount of particular radioactive isotope present at time t (dependent variable), -λ = decay rate (parameter). r(t) Note that the minus sign is used so that > > 0. (a) Using this notation, write a model for the decay of a particular radioactive iso- tope. (b) If the amount of the isotope present at t = 0 is ro, state the corresponding initial-value problem for the model in part (a).
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