Use logarithm

Question

If x is the atmospheric pressure (measured in millimeters of mercury) then the formula for altitude h(x) (measured in meters above sea level) is h(x)=(30T+8000)log(760/x) where T is temp in Celsius.

A. How high is a mountain with the temp is 5°c and an atmopheric pressure of 500mm of mercury?

 

B. Use algebra to find the atomopheric pressure of a mountain of 8900 meters high and temp is 0°c?

Answer 1

(a)

 

T = 5°C

x = 500 mm of Hg

 

h(x) = (30T + 8000)log(760/x) =[30(5) + 8000] log(760/500) m ≅ 1482 m

 

(b)

 

h = 8900 m

T = 0°C

8900 = [30(0) + 8000)]log(760/x)

8900 = 8000 log(760/x)

1.1125 = log(760/x)

10^1.1125 = 760/x

x = 760/10^1.1125 ≅ 58.7 mm of Hg