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Greenhouse gas emissions contribute significantly to global warming. This occurs during various operations, including the production, storage, and transportation of an inventory, but in some cases, the inventory itself becomes the emission source. Emissions from cattle dunk cakes, livestock slurry, manure, crude oil, and gasoline can be considered examples of this type of emissions. This paper proposes a mathematical formulation for a deteriorating inventory model utilizing the inventory as a source of emissions. The model is developed under inflation. Other activities, such as energy consumption for warehousing, are considered to be contributing to greenhouse gas emissions here. The rate of emissions from the product is exponentially governed by the rate of deterioration and the age of the material. The trapezoidal-type demand rate is considered using the Heaviside step function. Shortages are permitted but partially backlogged, and the backlogging rate is supposed to be decreasing exponentially with the increased waiting time. The numerical illustration of the model is provided to illustrate the mathematical expressions, and the effect of parametric variation is reported to give managerial insights. The results reveal that the greenhouse gas emissions are proportional to the variable rate of emissions cost and the deterioration rate. However, the increment in total emissions with respect to variable emissions cost increases with the deterioration rate. If the deterioration rate is negligible, total carbon emissions do not fluctuate much, but it increases rapidly if it is relatively high. The preservation technology is used to reduce deterioration and helps reduce emissions.