Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 9 - Section 9.3 - Logarithmic Functions and Models - Exercises - Page 657: 24

Answer

The half-life here is $27.726$ when $t=0$.

Work Step by Step

The exponential decay model is the following: $Q(t)=Q_0∗e^{-t_s∗k}$ Where $t_s∗k=\ln2$, and $t_s$ is the half-life at $t=0$ and k is constant. Here, $k=0.025$ $t_s∗k=ln2$ $t_s∗0.025=ln2$ $t_s=\frac{ln2}{0.025}=27.726$ Therefore the half-life here is $27.726$ when $t=0$.
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