Step 1: Concept
Mammalian cell culture media typically rely on a sodium bicarbonate-carbonic acid buffer system to maintain physiological pH (around 7.2 to 7.4), imitating blood serum chemistry.
Step 2: Carbon Dioxide Role
The bicarbonate buffer in the liquid medium exists in chemical equilibrium with gaseous carbon dioxide ($CO_2$) in the incubator's atmosphere:
$$CO_2 + H_2O \rightleftharpoons H_2CO_3 \rightleftharpoons H^+ + HCO_3^-$$
Maintaining a stable concentration of gaseous $CO_2$ prevents the loss of dissolved carbon dioxide from the medium, which would otherwise cause the pH to become dangerously alkaline.
Step 3: Standard Operating Values
The standard atmosphere in mammalian cell culture incubators is controlled at $37^\circ\text{C}$ with a constant, humidified supply of $5% - 10%$ $CO_2$ (most commonly $5%$).
Step 4: Conclusion
This directly corresponds to option (C).
Final Answer: (C)