Question

The atmospheric pressure at sea level is 14.7 lb/in2. This pressure is reduced by half for each 3.6 miles above sea level. Which graph correctly identifies the amount of atmospheric pressure based on height, in miles, above sea level?

Answer 1

The graph of atmospheric pressure based on height, in miles, above sea level is attached below.

Explanation:

The general exponential function is

`f(x)=ab^x`

Where a is initial value of the function and b is growth rate.

It is given that the atmospheric pressure at sea level is 14.7 lb/in2. This pressure is reduced by half for each 3.6 miles above sea level.

It means the initial value of the function is 14.7 and the growth factor is
`((1)/(2))^{(1)/(3.6)}`.

The required function is

`f(x)=14.7((1)/(2))^{(x)/(3.6)}`

Here, x is distance in miles above the sea-level and f(x) is atmospheric pressure in lb/in² at x miles above the sea-level.

The table of values is

x f(x)

0 14.7

3.6 7.35

7.2 3.675

10.8 1.8375

Therefore, the graph of atmospheric pressure based on height, in miles, above sea level is attached below.