Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - P.S. Problem Solving - Page 420: 14



Work Step by Step

$B=B_0a^{kt}$ Make $a=e$: $B=B_0e^{kt}$ When $t=0$ (in the beginning) $B=500$: $500=B_0e^{k·0}=B_0e^0$ $500=B_0(1)$ $B_0=500$ When $t=2$ (two hours later) $B=200$: $200=500e^{k·2}$ $\frac{200}{500}=e^{2k}$ $e^{2k}=0.4$ $\ln e^{2k}=\ln0.4~~$ (Use the Inverse Property: $\ln e^x=x$): $2k=\ln0.4$ $k=\frac{\ln0.4}{2}=-0.4581$ Finally we have: $B=500e^{-0.4581t}$
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