Gompertzian tumor growth. The growth fraction of a tumor declines exponentially over time (top). The growth rate of a tumor peaks before it is clinically detectable (middle). Tumor size increases slowly, goes through an exponential phase, and slows again as the tumor reaches the size at which limitation of nutrients or auto- or host regulatory influences can occur. The maximum growth rate occurs at 1/e, the point at which the tumor is about 37% of its maximum size (marked with an X). Tumor becomes detectable at a burden of about 10⁹ (1 cm³) and kills the patient at a tumor burden of about 10¹² (1 kg). Efforts to treat the tumor and reduce its size can result in an increase in the growth fraction and an increase in growth rate.