## Calculus 10th Edition

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 $P(35000) =30e^{-35000ln(2)/18000}=7.794 inches$