We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk origins and grows by continuous gas infall. The gas infall rate is parametrized by the Gaussian formula with one free parameter: infall-peak
time $t_p$. The Kennicutt star formation law is adopted to describe how much cold gas turns into stars. The gas outflow process is also considered in our model. We find that, at given galactic stellar mass $M_*$, model adopting late infall-peak time $t_p$ results in blue colors, low metallicity, high specific star formation rate and high gas fraction, while gas outflow rate mainly influences the gas-phase metallicity and star formation efficiency mainly influences the gas fraction. Motivated by the local observed scaling relations, we construct a mass-dependent model by assuming low mass galaxy has later infall-peak time $t_p$ and larger gas outflow rate than massive systems. It is shown that this model can be in agreement with not only the local observations, but also the observed correlations between specific star formation rate and galactic stellar mass $SFR/M_* sim M_*$ at intermediate redshift $z<1$. Comparison between the Gaussian-infall model and exponential-infall model is also presented. It shows that the exponential-infall model predicts higher star formation rate at early stage and lower star formation rate later than that of Gaussian-infall. Our results suggest that the Gaussian infall rate may be more reasonable to describe the gas cooling process than the exponential infall rate, especially for low-mass systems.
