Use your model to determine the atmospheric pressure at an altitude of 3700 meters.

Question

Atmospheric pressure decreases by about 15% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 3700 meters.
(Express your answer in millibars rounded correctly to the nearest tenth.)

Answer 1

The general model will be:

 

pressure = A * e ^(-h*b)

 

A is the pressure at sea level

h is the height above sea level

 

You are given that when h=1000 meters, the pressure as decreased by 15%.  This means that it is 85% if the level at sea level, so:

 

A * e ^(-1000b) = 0.85*A

 

dividing by A gives:

e^(-1000b) = 0.85

 

Take ln of both sides:

 

-1000b = -0.16252

b=0.00016

 

So the pressure is given by:

 

pressure = 1013 * e ^(-0.00016*h)

 

At an altitude of 3700 meters:

pressure = 1013 * e ^{(-0.00016*3700}) = 555.2 millibars