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Some people think that it is implausible that humans can be affecting the amount of CO₂ in the atmosphere because the atmosphere is so big and we are so small. The total mass of the atmosphere is very large – about 5 x 10¹⁸ kg. But CO₂ is a fairly small fraction of this – about 6 x 10^-4 of its mass.

According to the website on carbon footprints, the average amount of CO₂ produced by a person in the US is about 20 metric tons per person per year. (One metric ton is 10³ kg.) If every person in the world produced this much CO₂ every year, how long would it take to increase the amount of CO2 in the atmosphere by 20%? (This is oversimplified, but gives us a reasonable idea of whether it is at all plausible that human produced CO₂ can be significant.)

Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your reasoning, not on your answer.

Page last modified December 29, 2010: G45