Question

mountain climbers know that the atmospheric pressure and the boiling point of water decrease. we measure the pressure in kilopascals (kpa) and the atmospheric pressure is 100 kpa at sea level and decreases by about 12 kpa for each kilometer above sea level. estimate the atmospheric pressure (in kpa) at the peak of mt. evans, 4.4 km above sea level.

Explanation:

Step1: Identify the initial pressure and rate of change

The initial pressure at sea - level is $P_0 = 100$ kPa and the rate of decrease is $12$ kPa per kilometer.

Step2: Set up the linear - equation formula

The linear - equation for pressure $P(x)$ as a function of altitude $x$ (in kilometers) is $P(x)=P_0 - 12x$.

Step3: Substitute the given altitude

We want to find the pressure at $x = 4.4$ km. Substitute $x = 4.4$ into the equation: $P(4.4)=100-12\times4.4$.

Step4: Calculate the result

First, calculate $12\times4.4 = 52.8$. Then, $P(4.4)=100 - 52.8=47.2$ kPa.

Answer:

$47.2$ kPa