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$(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} $

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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}$

$\log \large\frac{1}{2}$$=6000 K$

Now $ \log P \bigg]_{P_0}^{P}=\large\frac{\log (1/2)}{6000} \times h \bigg]_0^h$

$ \log \frac{P}{P_0} =\large\frac{h \log (1/2)}{6000}$

$P=P_0 \bigg(\large\frac{1}{2}\bigg) ^{\Large\frac{h}{6000}}$

Hence d is the correct answer.

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