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It's very hard to argue without numerical data, but the graph on the Wikipedia version of the graph seems to increase linearly to my eyes: https://en.wikipedia.org/wiki/Keeling_Curve (Edit: No, I can see what you mean; the graph is steeper from 2010–2020 than from 2000–2010.)

(To anyone a bit confused, the Keeling graph is the cumulative amount of CO2 in the atmosphere, so emissions are the first derivative of this graph.)

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> ... so emissions are the first derivative of this graph

Not exactly. There is a net sink of emissions every year into the land & ocean, so d(CO2)/dt = emissions minus the net sinks, roughly. See the graph on CO2 partitioning [0]. A lot of research goes into whether these sinks continue at their current rate of removal.

[0] https://en.wikipedia.org/wiki/Atmospheric_carbon_cycle#Anthr...

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