Final answer:
The two processes that facilitate the biological carbon cycle are photosynthesis and cellular respiration, with photosynthesis converting CO2 to organic compounds and cellular respiration converting organic compounds back to CO2.
Step-by-step explanation:
The two processes performed by living organisms that facilitate the biological carbon cycle are photosynthesis and cellular respiration.
Photosynthesis is the process by which autotrophs, like plants and certain microbes, convert carbon dioxide and water into glucose and oxygen using the sun's energy.
Cellular respiration is the process by which both autotrophs and heterotrophs convert the energy stored in glucose back into carbon dioxide and water, releasing energy that they can use for their metabolic processes.
These two processes are interconnected parts of the carbon cycle, rapidly exchanging carbon between the atmosphere and the organisms in ecosystems.