Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.4 Exponential Growth and Decay - Exercises - Page 349: 14


$ k\approx 0.071$

Work Step by Step

Since the exponential decay is given by $$ P(t)=P_0 e^{-kt}, \quad k\gt 0$$ then we have $$ P(t)=10 e^{-kt}.$$ At $ t=17$, $ P(17)=3$, so: $$ P(17)=10 e^{-17k}=3\Longrightarrow k=-\frac{\ln(3/10)}{17}\approx 0.071.$$
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