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.
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
Thank you.
You are welcome
Yes, you are correct! The presence of the multiplication operation suggests that the equation is exponential. In an exponential equation, the variable is the exponent, and the base (in this case, 0.88) is raised to that exponent. This means that as the value of x increases, the base (0.88) is repeatedly multiplied by itself, causing the exponential decrease in air pressure.
In contrast, if the equation involved addition or subtraction of x (such as y = 1013 - 0.12x), it would indicate a linear relationship, where the change in air pressure would be constant for each increase in elevation.
So, when you see an equation with multiplication or division involving a variable raised to an exponent, it is often an indication of an exponential relationship.