Why can plants produce carbon dioxide as a product of cellular respiration

Because it goes through a process called photosynthesis

   Plants go through cellular respiration when they are not using photosynthesis for their metabolic needs; when they are not in need of food.
During cellular respiration, the cell uses oxygen to break down sugar. Breaking down sugar produces the energy the organism needs. This is very similar to wood burning in a fire. As the wood burns, it combines with oxygen and releases heat energy and carbon dioxide. When the cell uses oxygen to break down sugar, oxygen is used, carbon dioxide is produced, and energy is released.

C14 dating since carbon is present in both living and no living objects .