A continuum model describing the steady-state actin dynamics of the cytoskeleton of living cells has been developed to aid in the interpretation of photoactivated fluorescence experiments. In a simplified cell geometry, the model assumes uniform concentrations of cytosolic and cytoskeletal actin throughout the cell and no net growth of either pool. The spatiotemporal evolution of the fluorescent actin population is described by a system of two coupled linear partial-differential equations. An analytical solution is found using a Fourier-Laplace transform and important limiting cases relevant to the design of experiments are discussed. The results demonstrate that, despite being a complex function of the parameters, the fluorescence decay in photoactivated fluorescence experiments has a biphasic behavior featuring a short-term decay controlled by monomer diffusion and a long-term decay governed by the monomer exchange rate between the polymerized and unpolymerized actin pools. This biphasic behavior suggests a convenient mechanism for extracting the parameters governing the fluorescence decay from data records. These parameters include the actin monomer diffusion coefficient, filament turnover rate, and ratio of polymerized to unpolymerized actin.