  We present analytical solutions to the steady state
injection-condensation-coagulation equation of aerosols in the atmosphere.
These solutions are appropriate under different limits but more general than
previously derived analytical solutions. For example, we provide an analytic
solution to the coagulation limit plus a condensation correction. Our solutions
are then compared with numerical results. We show that the solutions can be
used to estimate the sensitivity of the cloud condensation nuclei number
density to the nucleation rate of small condensation nuclei and to changes in
the formation rate of sulfuric acid.
