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

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

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)`