Just for the sake of correctness:

The used Keeling data are to be understood as results of measurements done in the middle of the respective month - so, for working with the precise data one has to replace the second line of my code by:

dataKeeling = TimeSeries[{DateObject[{#1, #2, 15}], #3} & @@@ dataRaw[[62 ;; -9, {1, 2, 9}]]];

This means a shift in the data of 15 days. Sorry for this flaw!

Hi Henrik, Thanks for your great comment.

This posting was intended to show that if CO2 emissions increase 'linearly,' then the CO2 concentration will increase 'quadratically,' contrary to a common misunderstanding that the CO2 concentration will also increase 'linearly.' The CO2 concentration will increase much faster than we think. Your analysis confirms that CO2 emission has been increased linearly and therefore CO2 concentration has been increasing quadratically.

The correct title should be "Linear increase in CO2 emissions will result in a quadratic increase in CO2 concentration.

This posting did not consider the outflow (i.e., CO2 sink or absorption). I have posted another update to demonstrate that the CO2 sink has been increasing.
https://community.wolfram.com/groups/-/m/t/2927367