Answer
(a) 64.48 kPa
(b) 39.91 kPa
Work Step by Step
(a) $\frac{dP}{dh} = kP$
The solution to this equation is:
$P(h) = P(0)e^{kh}$
We can find $k$:
$P(h) = P(0)e^{kh}$
$P(1000) = 101.3~e^{1000k} = 87.14$
$e^{1000k} = \frac{87.14}{101.3}$
$1000k = ln(\frac{87.14}{101.3})$
$k = \frac{ln(\frac{87.14}{101.3})}{1000}$
$k = -0.00015057$
Then:
$P(h) = P(0)e^{-0.00015057~h}$
We can find the pressure $P$ when $h = 3000~m$:
$P(h) = P(0)e^{-0.00015057~h}$
$P(3000) = 101.3~e^{(-0.00015057)~(3000)}$
$P(3000) = 64.48$
(b) We can find the pressure $P$ when $h = 6187~m$:
$P(h) = P(0)e^{-0.00015057~h}$
$P(6187) = 101.3~e^{(-0.00015057)~(6187)}$
$P(6187) = 39.91$
