 Solution

Holding emissions at $E_{00}=8.069\mathrm{GtC}\mathrm{y}{\mathrm{r}}^{-1}$ gives equilibrium concentrationFor time $t$ since 2000,It increases monotonically on the same 200-year timescale and reaches about $654.07\mathrm{ppmv}$ in 2500. The limiting, and hence peak asymptotic, warming isIn 2500 the equilibrium warming is about $3.69\mathrm{K}$, still below that asymptote. A stable thermal adjustment much faster than the carbon timescale follows this slow approach with a short lag and has the same limiting warming. These are predictions of the specified linear reservoir model, not a claim that constant real emissions produce a finite universal atmospheric equilibrium.