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# Observation show that rate of change of atmosphere pressure P with attitude h is proportional to pressure. Assume that pressure at 6000 meter is half of its value $P_0$ at sea level, find formula for pressure at any height.

$(a)\;P=p. \frac{h}{6000} \\ (b)\;P= 3000 p.h \\ (c)\;P= P.(\frac{1}{2})h \\ (d)\;P=P. (\frac{1}{2})^{h/6000}$

given $\large\frac{dp}{dh}$$=KP \large\frac{dP}{P}$$=K dh$
Integrate $\ln P \bigg]_{P_0}^{P/o/2}=k h \bigg]_0^{6000}$