Answer
a) $\approx$ $64.5$ kPa.
b) $\approx$ $39.9$ kPa.
Work Step by Step
a)
Let $P(h)$ be the pressure at altitude $h$
Then
$\frac{dP}{dh}$ = $kP$
$P(h)$ = $P(0)e^{kh}$
$P(h)$ = $101.3e^{kh}$
$P(1000)$ = $101.3e^{1000k}$
$87.14$ = $101.3e^{1000k}$
$k$ = $\frac{1}{1000}\ln{\frac{87.14}{101.3}}$
$P(h)$ = $101.3e^{\frac{h}{1000}\ln{\frac{87.14}{101.3}}}$
$P(3000)$ = $101.3e^{\frac{3000}{1000}\ln{\frac{87.14}{101.3}}}$
$P(3000)$ $\approx$ $64.5$ kPa.
b)
$P(6187)$ = $101.3e^{\frac{6187}{1000}\ln{\frac{87.14}{101.3}}}$
$P(6187)$ $\approx$ $39.9$ kPa.
