Two-reservoir carbon pulse response ($C(t)=(1+e^{-2kt})/2$)

Equal-capacity reservoirs exchanging carbon symmetrically preserve their total burden. Their difference decays at rate $2k$, so a pulse into one reservoir leaves one half there permanently unless an external sink is added. Coupling this response to a faster first-order thermal model produces an initial warming followed by relaxation to a nonzero asymptote.