Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 5 - Logarithmic Functions - 5.2 Logarithms and Exponential Models - Exercises and Problems for Section 5.2 - Exercises and Problems - Page 200: 11

Answer

$$14 e^{-0.2079\ t}$$

Work Step by Step

Recall the property $(a^m)^n=a^{mn}$, so the equation can be rewritten as $$Q=14(0.862)^{1.4 t}=14 (0.8123)^t=14 (e^{\ln 0.8123} )^t ~~~~(1)$$ Evaluating $\ln 0.8123$ yields $-0.2079$. Therefore, the equation (1) can be written as $Q=14 (e^{\ln 0.8123} )^t=14 e^{-0.2079\ t}$
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