Question

A meteorologist is monitoring the atmospheric pressure as his height above sea level varies. The meteorologist determines that the atmospheric pressure decreases by 12% for each additional kilometer the city is above sea level. The atmospheric pressure at sea level is 103 kPa (kilopascals). Define a function, p , that determines the atmospheric pressure (in kPA) in terms of the number of kilometers the city is above sea level, n .

Answer 1

Answer:

The function $p(n)$ is represented by $p(n) = 103\cdot (0.88)^{n}$.

Step-by-step explanation:

Statement indicates that atmospheric pressure decreases exponentially when height above sea level is increased. This fact is represented by the following model:

$p(n) = p_{o}\cdot r^{n}$ (Eq. 1)

Where:

$p_{o}$ - Atmospheric pressure at sea level, measured in kilopascals.

$r$ -Atmospheric pressure decrease rate, dimensionless.

$n$ - Height above sea level, measured in kilometers.

$p(n)$ - Current pressure, measured in kilopascals.

If we know that $p_{o} = 103\,kPa$ and $r = 0.88$, the function $p(n)$ is represented by:

$p(n) = 103\cdot (0.88)^{n}$