Plant's produce oxygen, to explain this you would state that the plant uses CO2 from the air and removes the carbon and then release breathable O2 into the atmosphere. To test this you could use a small fern and put it in a sealed container of some kind big enough to hold it, then add a burning candle in the container with the plant, since we know fire burms O2 and creates CO2 the plant should use the CO2 and create more O2 keeping the fire from burning out from lack of oxygen
Ways carbon is added to the atmosphere is through the respiration of animals, the decay of plant matter, combustion of organic materials, and volcanic eruptions.
