All cells derive nutrition by absorbing some chemical and energy resources from the environment; these resources are used by the cells to reproduce the chemicals within them, which in turn leads to an increase in their volume. In this study we introduce a protocell model exhibiting catalytic reaction dynamics, energy metabolism, and cell growth. Results of extensive simulations of this model show the existence of four phases with regard to the rates of both the influx of resources and cell growth. These phases include an active phase with high influx and high growth rates, an inefficient phase with high influx but low growth rates, a quasistatic phase with low influx and low growth rates, and a death phase with negative growth rate. A mean field model well explains the transition among these phases as bifurcations. The statistical distribution of the active phase is characterized by a power law, and that of the inefficient phase is characterized by a nearly equilibrium distribution. We also discuss the relevance of the results of this study to distinct states in the existing cells.