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.

Question

$(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} $