College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.5 - Page 507: 60

Answer

In an exponential decay model, the time needed for the substance to decay to half of its initial quantity.

Work Step by Step

Half-time is related to the Exponential decay model: $A=A_{0}e^{kt} \quad (k<0)$ (where $A_{0}$ is the initial quantity, and $A$ is the quantity after time t) ----------- At some point of time, the quantity $A$ will become half the initial quantity, $A_{0}$. (The initial quantity decays to half) The time needed for this to happen is the half-life of the substance. It is calculated by solving $0.5A_0=A_{0}e^{kt}$ for t
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