Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - Review Exercises: 27


7.794 inches

Work Step by Step

We are given that, $$\frac{dP}{dh}=kp$$ Therefore, $$\int \frac{dP}{p}=\int kdh$$ $$ln|P| = kh+C'$$ Or, $$P=Ce^{kh}$$ where $C=e^{C'}$ We are also given that $$P(0)=30, P(18000)=15$$ Therefore, $30 =Ce^0$ or $$C=30$$ And $30e^{18000k}=15$ Therefore, $$k=-\frac{ln(2)}{18000}$$ Thus, $P(h)=Ce^{kh}=30e^{-hln(2)/18000}$ And $P(35000) =30e^{-35000ln(2)/18000}=7.794 inches$
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