Question

mountain climbers know that the atmospheric pressure and the boiling point of water decrease as elevation increases. although these properties depend on many factors, in this exercise, we find approximate linear models that relate them. we measure the pressure in kilopascals (kpa) and the boiling point in degrees celsius (°c). at a pressure of 100 kpa the boiling point of water is 100°c and drops by about 3.75°c for each 10 kpa drop in atmospheric pressure. find a linear function g that models the boiling point of water at an atmospheric pressure of x kilopascals. g(x) = estimate the boiling point of water (in °c) if the atmospheric pressure is 74 kpa.

Explanation:

Step1: Find the slope

The slope $m = \frac{-3.75}{10}=- 0.375$.

Step2: Use point - slope form

The point is $(100,100)$, so $g(x)=100-0.375(x - 100)=-0.375x + 137.5$.

Step3: Calculate boiling point at 74 kPa

Substitute $x = 74$ into $g(x)$: $g(74)=-0.375\times74 + 137.5=109.75$.

Answer:

$g(x)=-0.375x + 137.5$; $109.75$