(a) Consider the initial-value problem dA/dt = kA, A(0) = A 0 as the model for the...

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(a) Consider the initial-value problem dA/dt = kA, A(0) = A₀ as the model for the decay of a radioactive substance. Showthat, in general, the half-life T of the substance is T = 2(ln 2)/k.

(b) Show that the solution of the initial-value problem in part (a) can be written A(t) = A₀2^-t/T.

(c) If a radioactive substance has the half-life T given in part (a), how long will it take an initial amount A₀ of the substance to decay to 1/8 A₀?

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A First Course in Differential Equations with Modeling Applications

ISBN: 978-1305965720

11th edition

Authors: Dennis G. Zill

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Question Posted: Jul 13, 2018 01:01 PM

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(a) Consider the initial-value problem dA/dt = kA, A(0) = A 0 as the model for the...

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a The solution of dAdt kA is At A 0 e kt Letting A 12A 0 and ...View the full answer

A First Course in Differential Equations with Modeling Applications

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