A target of 80% cuts in emissions by the year 2050 has been floated as a goal that would enable us to avoid the worst of climate change. You can see that scenario, for example, in the ISAM model. One formula for an exponential decline is:
C(t) = C(0) x e-k t
where C is the rate of carbon emissions, C(0) is the initial rate, C(t) is the rate at time t, k is approximately the rate of decline (NOT in %), and e is the exponential constant (≈ 2.718). Assuming we start in 2015 and reduce emissions by 80% by 2050 (in 35 years), what annual rate of emissions cuts would be required, in percent?