Question

The kilopascal is a unit of measure for atmospheric pressure. Suppose the atmospheric air pressure at sea level is about 101 kilopascals. For every​ 1000-m increase in​ altitude, the pressure decreases about 11.3 ​%. What is the approximate pressure at an altitude of 2000 ​m?

The pressure at an altitude of 2000 m is about ___ kilopascals.

Answer 1

The pressure at an altitude of 2000 m is about 79.46 kilopascals.

Explanation:

The atmosphered air pressure, for each n 1000m increase in altitude, has the following format:

`A(n) = A(0)(1-r)^(n)`

In which A(0) is the pressure at sea level and r is the decrease rate, as a decimal.

Suppose the atmospheric air pressure at sea level is about 101 kilopascals.

This means that
`A(0) = 101`.

For every​ 1000-m increase in​ altitude, the pressure decreases about 11.3 ​%.

This means that
`r = 0.113`

So

`A(n) = A(0)(1-r)^(n)`

`A(n) = 101(1-0.113)^(n)`

`A(n) = 101(0.887)^(n)`

What is the approximate pressure at an altitude of 2000 ​m?

2000/1000 = 2.

So this is A(2).

`A(n) = 101(0.887)^(2) = 79.46`

The pressure at an altitude of 2000 m is about 79.46 kilopascals.