 Solution

The term $b_{1}E$ is the effective atmospheric addition from ongoing emissions. Its coefficient $0.25ppmv/GtC$ is about half the full-retention estimate $0.47ppmv/GtC$, so the model implicitly removes or partitions some emitted carbon promptly. The term $-b_0(C-C_0)$ represents slower net uptake of the excess by other reservoirs; its relaxation time is $b_0^{-1}=200$ years. Both terms have units of ppmv per year.

Thousands of years at constant $E_0$ erase the initial transient, givingThe reference $C_0$ is the zero-anthropogenic-emission equilibrium, not the equilibrium when the stated small persistent emissions are present.