Atmospheric pressure decreases by about 138 for every 1000 m

Atmospheric pressure decreases by about 13.8% 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 pressures at an altitude of 2550 meters. (Express your answer in millibars rounded corrrectly to the nearest tenth.)

__________millibars

Solution

Answer:

Let P(h) denotes the the atmospheric pressure at a given altitude in thousands of meters.

P(h) = 1013(1-13.2%)^h/1000, where a₀ = initial measure, b = rate of change, h = change in height

P(h) = 1013(1-0.132)^h/1000

P(h) = 1013(0.868)^h/1000

when h = 2550 meters

P(2550) = 1013(0.868)^2550/1000

P(2550) = 1013(0.868)^2.55

P(2550) 706.04