Question

The pressure of earth's atmosphere at sea level is approximately 1000 millibars and decreases exponentially with elevation. At an elevation of 30,000ft, the pressure is one-third of the sea level pressure. At what elevation is the pressure half of the sea-level pressure? At what elevation is it 1% of the sea-level pressure?

Answer 1

@electrokid @abb0t

Answer 2

decreases exponentially.
so, let the pressure at a height "h" be expressed as:
\[P(h)=P_0e^{-kh}\]
where P0 = pressure at height h=0
and k = an exponential const.
first obtain k using P(30,000)=1000/3

Answer 3

then, find "h" such that P(h)=1000*(1/100)

Answer 4

we can re-write our function as:
\[
-kh = \ln(P/P_0)\implies kh=\ln(P_0/P)\\
k(30000)=\ln(3)\implies\text{find k}\\
(?)h=\ln(100)
\]