1.) one gigatonne=1 GT=109 metric tonnes.
1 GT of carbon roughly corresponds to 3.67 GT CO2.
1 ppmv CO2 in the atmosphere roughly corresponds to 7.8 GT CO2 (or 2.1 GT carbon)

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2.) Plants convert a total of 120 GT C annually. they also respire 60 GT C. Net photosynthesis conversion is 60 GT C anually.

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3)The coefficients were determined from CDIAC data.(http://cdiac.ornl.gov/ndps/ndp006.html)using Microsoft Excel. Coefficients were taken from the poly 4 trend line The fourth order polynomial offers a better fit to the data then the exponential fit which seems to overestimate the recent data.

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4).The general solution to

is as follows. Let

then,

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