Question

The air pressure at sea level is generally about 1013 hPa (hectoPascals). For every kilometer that you go up in elevation, the air pressure decreases by 12%. Write an equation that describes the air pressure when the elevation is x kilmoeters above the sea level.

The answer is y = 1013(0.88)^x

The 0.88 is from the 12% (100% - 12% is 88% which is .88 as a decimal)

My question is: how do I know, just by reading this, that it is exponential? Is it because of the multiplication of the .88? Because exponential is multiplication and linear is addition of the same constant amount?

Thank you.

Answer 1

Yes, it would be because of the repeated multiplication by .88
suppose we show a few steps

after 1 km : Pr = 1013(.88)
after 2 km : Pr = 1013(.88)(.88) = 1013 (.88)^2
after 3 km : Pr = 1013(.88)^2 (.88) = 1013 (.88)^3
etc , for
after x km : Pr = 1013 (.88)^x

Answer 2

Thank you.

Answer 3

You are welcome