The relation between CO2 emissions and atmospheric CO2 concentration has traditionally been treated with more or less complex models with several boxes. Our approach is motivated by the question of how much CO2 must necessarily be absorbed by sinks. Observations lead to the model assumption, that carbon sinks like oceans or biosphere are linearly dependent on CO2 concentration on a decadal scale. In particular this implies the falsifiable hypothesis that oceanic and biological CO2 buffers have not significantly changed in the past 50 years and are not saturated in the forseeable future. The simple model with 2 parameters explains very well the CO2 emission and historical CO2 concentration data. The model gives estimates of the natural emissions, the pre-industrial CO2 equilibrium concentration levels, the half-life time of an emission pulse, and the future CO2 concentration level from a given emission scenario. This is validated by an ex-post forecast of the last 20 years. The important result is that with the stated polices scenario of the IEA future CO2 concentrations will not rise above 475 ppm. The model is compared with the Carbon modul of the Bern model, mapping their complex IRFs to a single time variant parameter.