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Hi Rofat,
Without having seen your model, I can't speculate on why this is happening. But I can certainly imagine a situation where emissions growth is more rapid than growth in energy demand - for example, how is the growing energy demand being met? If additional demands are being met using increasingly carbon-intensive fuels, you would see faster growth in emissions than you would see for demand.
Have a look in your model to see how LEAP meets growing household demand. Exploring the 'Results' view will help you identify the source of your emissions growth. Try displaying household demand by fuel, for example, too see how demands for each fuel type change during your scenario.
Good luck,
Taylor