A key uncertainty in galaxy evolution is the physics regulating star formation , ranging from small-scale processes related to the life-cycle of molecular clouds within galaxies to large-scale processes such as gas accretion onto galaxies . We study the imprint of such processes on the time-variability of star formation with an analytical approach tracking the gas mass of galaxies ( ‘ ‘ regulator model ’ ’ ) . Specifically , we quantify the strength of the fluctuation in the star-formation rate ( SFR ) on different timescales , i.e . the power spectral density ( PSD ) of the star-formation history , and connect it to gas inflow and the life-cycle of molecular clouds . We show that in the general case the PSD of the SFR has three breaks , corresponding to the correlation time of the inflow rate , the equilibrium timescale of the gas reservoir of the galaxy , and the average lifetime of individual molecular clouds . On long and intermediate timescales ( relative to the dynamical timescale of the galaxy ) , the PSD is typically set by the variability of the inflow rate and the interplay between outflows and gas depletion . On short timescales , the PSD shows an additional component related to the life-cycle of molecular clouds , which can be described by a damped random walk with a power-law slope of \beta \approx 2 at high frequencies with a break near the average cloud lifetime . We discuss star-formation ‘ ‘ burstiness ’ ’ in a wide range of galaxy regimes , study the evolution of galaxies about the main sequence ridgeline , and explore the applicability of our method for understanding the star-formation process on cloud-scale from galaxy-integrated measurements .