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: 20

Answer

$Q(t)=2000*e^{-0.1386t}$

Work Step by Step

The exponential decay model is the following: $Q(t)=Q_0*e^{-t_s*k}$ Where $t_s*k=\ln2$, where $t_s$ is the half-life at $t=0$ and $k$ is constant. $Q_0=2000$ $t_s*k=\ln2$ $5*k=\ln2$ $k=\frac{\ln2}{5}=0.1386$ Therefore the model follows the equation of: $Q(t)=2000*e^{-0.1386t}$
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