We quantify the relative roles of natural and anthropogenic influences on the growth rate of atmospheric CO2 and the CO2 airborne fraction, considering both interdecadal trends and interannual variability. A combined ENSO-Volcanic Index (EVI) relates most (~75%) of the interannual variability in CO2 growth rate to the El-Niño-Southern- Oscillation (ENSO) climate mode and volcanic activity. Analysis of several CO2 data sets with removal of the EVI-correlated component confirms a previous finding of a detectable increasing trend in CO2 airborne fraction (defined using total anthropogenic emissions including fossil fuels and land use change) over the period 1959-2006, at a proportional growth rate 0.24% y-1 with probability ~0.9 of a positive trend. This implies that the atmospheric CO2 growth rate increased slightly faster than total anthropogenic CO2 emissions. An extended form of the Kaya identity relates the increase in the CO2 growth rate (1.9% y-1 over 1959-2006) to the growth rates of four global driving factors: population (contributing +1.7% y-1); per capita income (+1.8% y-1); the total carbon intensity of the global economy (-1.7% y-1); and airborne fraction (averaging +0.2% y-1 with strong interannual variability). Together, the recent (post-2000) increase in growth of per capita income and decline in the negative growth (improvement) in the carbon intensity of the economy will drive a significant acceleration in the CO2 growth rate over coming decades, unless these recent trends reverse. To achieve an annual reduction rate in total emissions of -2% y-1 (which would halve emissions in 35 years) in the presence of a per-capita income growth rate of 2% y-1 and a population growth rate of 1% y-1, it is necessary to achieve a decline in total carbon intensity of the economy at a rate of around -5% y-1, three times the 1959-2006 average.