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(a) Consider the initial-value problem dA/dt kA, A(0) = Ao as the model for the decay of a radioactive substance. Show that, in general, the half-life T of the substance is T = -(ln(2))/k. (b) Show that the solution of the initial-value problem in part (a) can be written A(t) = Ao2-/T. (c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount Ao of the substance to decay to Ao/8? =

(a) Consider the initial-value problem dA/dt kA, A(0) = Ao as the model for the decay of a radioactive substance. Show that, in general, the half-life T of the substance is T = -(ln(2))/k. (b) Show that the solution of the initial-value problem in part (a) can be written A(t) = Ao2-/T. (c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount Ao of the substance to decay to Ao/8? =

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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= = (1) (a) Consider the initial-value problem dA/dt kA, A(0) Ao as the model for the decay of a radioactive substance. Show that, in general, the half-life T of the substance is T = -(ln(2))/k. (b) Show that the solution of the initial-value problem in part (a) can be written A(t) = Ao2-t/T. (c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount Ao of the substance to decay to Ao/8?
Transcribed Image Text:= = (1) (a) Consider the initial-value problem dA/dt kA, A(0) Ao as the model for the decay of a radioactive substance. Show that, in general, the half-life T of the substance is T = -(ln(2))/k. (b) Show that the solution of the initial-value problem in part (a) can be written A(t) = Ao2-t/T. (c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount Ao of the substance to decay to Ao/8?
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