Question

atmospheric pressure is 100 kpa at sea level and decreases by about 12 kpa for each kilometer increase in elevation. find a linear function f that models atmospheric pressure (in kpa) at elevation h (in km) above sea level. then find the atmospheric pressure (in kpa) at the peak of mt. evans, 4.4 km above sea level.

Explanation:

Step1: Recall linear - function form

The general form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Let $x$ be the elevation above sea - level in kilometers and $y$ be the atmospheric pressure in kPa.

Step2: Determine the slope

The pressure decreases by about 12 kPa for each kilometer increase in elevation. So, the slope $m=- 12$.

Step3: Determine the y - intercept

At sea - level ($x = 0$), the pressure is 100 kPa. So, when $x = 0$, $y = 100$, and the y - intercept $b = 100$.

Step4: Write the linear function

Substitute $m=-12$ and $b = 100$ into $y=mx + b$. We get $y=-12x + 100$.

Answer:

$f(x)=-12x + 100$