Multiple phenotypic states often arise in a single cell with different gene-expression states that undergotranscription regulation with positive feedback. Recent experiments show that, at least in E. coli, the genestate switching can be neither extremely slow nor exceedingly rapid as many previous theoretical treatments assumed. Rather, it is in the intermediate region which is difficult to handle mathematically. Under this condition,from a full chemical-master-equation description we derive a Fluctuating-rate model in which the protein copy number, for a given gene state, follows a deterministic mean-field description while the protein-synthesis rates fluctuate due to stochastic gene state switching. The simplified kinetics yields anonequilibrium landscape function, which,similar to the energy function for equilibrium fluctuation, provides the leading orders of fluctuations around each phenotypic state, as well as the transition rates between the two phenotypic states. This rate formula is analogous to Kramers? theory for chemical reactions.