= Solution
The real <carbon cycle> has multiple reservoirs and adjustment times, rather than one universally exponential removal process. Air-sea exchange, ocean mixing and carbonate chemistry give a long-lived atmospheric tail; uptake also changes with <temperature>, circulation and carbon loading. For example, a warming ocean can absorb less additional <carbon dioxide>, so a fixed $b_0$ omits a potentially positive climate-carbon feedback. Terrestrial vegetation and soil responses provide further examples. \b[One missing feature is the dependence of carbon uptake on the changing state of the ocean and climate.]
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