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