We present a minimal model for the global carbon cycle of the Earth containing the reservoirs mantle, ocean floor, continental crust, biosphere, and the kerogen, as well as the combined ocean and atmosphere reservoir. The model is specified by introducing three different types of biosphere: procaryotes, eucaryotes, and complex multicellular life. During the entire existence of the biosphere procaryotes are always present. 2 Gyr ago eucaryotic life first appears. The emergence of complex multicellular life is connected with an explosive increase in biomass and a strong decrease in Cambrian global surface temperature at about 0.54 Gyr ago. In the long-term future the three types of biosphere will die out in reverse sequence of their appearance. We show that there is no evidence for an implosion-like extinction in contrast to the Cambrian explosion. In dependence of their temperature tolerance complex multicellular life and eucaryotes become extinct in about 0.8-1.2 Gyr and 1.3-1.5 Gyr, respectively. The ultimate life span of the biosphere is defined by the extinction of procaryotes in about 1.6 Gyr.