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$C=N\left(\frac{GDP}N\right)\left(\frac{E}{GDP}\right)\left(\frac{C}E\right)$ $$C=N\left(\frac{GDP}N\right)\left(\frac{E}{GDP}\right)\left(\frac{C}E\right)$$  The *Kaya Identity* is a member of the I=PAT family of identities, which are used to describe human impact on the environment. The *Kaya Identity* in particualr is used is quantify CO₂ emissions at any given point time and scale. It is a non-cumulative formula, however it can be integrated over $C$ to yield cumulative emissions for any given timescale.