IPCC has been deceiving public on carbon cycle from 1990 First Assessment Report. The article contains only one technical passage in need of more accurate rendering. Engineering and physics textbooks often advise students this way: if If you are dealing with an unfamiliar process or system, try to represent it by the first two members of Taylor’s series. In the case of the atmospheric CO2 concentration, this gives
C'(t) = -λC(t)
where C is the surplus (over the equilibrium) CO2 concentration, and the constant > 0. This is the equation for exponential decay:
C(t) = C(0)exp(-λt)
The value h = ln(2)/λ is the half-life of the surplus concentration. Of course, this is just one reasonable approach to the problem. More research could have shown that the half-life is not constant, but varies depending on time, historical emissions, sinks saturation, or other variables. But so far, neither research nor observations contradict hypothesis of constant half-life of surplus CO2.