Step 1: Understand what a dissolved oxygen (DO) reading of zero means.
The DO probe measures the oxygen dissolved in the broth at that instant. A reading of zero means the dissolved oxygen is being used up as fast as it enters, so none is left over at any moment.
It does not mean oxygen has stopped entering the vessel, aeration is still continuous, and it does not by itself mean the cells are dead.
Step 2: Compare oxygen supply and oxygen demand.
Dissolved oxygen concentration is set by the balance of two rates: the oxygen transfer rate (OTR), how fast oxygen crosses from the sparged air into the liquid, and the oxygen uptake rate (OUR), how fast the growing cells consume that dissolved oxygen.
When cell density and oxygen demand (OUR) rise to meet or exceed what the aeration system can supply (OTR), every molecule of oxygen that dissolves is consumed almost at once, and the steady DO reading drops to zero.
Step 3: Rule out the wrong options.
(A) is wrong because a dead culture stops consuming oxygen, so DO would rise back up toward the saturation value, not stay at zero; a live, actively respiring culture is what keeps DO pinned at zero.
(B) is wrong because running out of carbon source would also stop respiration, which would raise DO, not lower it, and there is no information here about carbon depletion.
(D) is wrong because if growth did not depend on dissolved oxygen, the cells would not be pulling oxygen out of solution at all, and DO would simply track the supply rate instead of sitting at zero.
Step 4: Confirm the correct inference.
Since DO is zero while aeration continues, the cells are using oxygen faster than it can be supplied. Growth is now capped by how much oxygen is available, not by substrate or biomass.
This matches option (C).
Final Answer:
A DO reading of zero under continuous aeration shows that oxygen demand has outrun oxygen supply, so the culture growth becomes oxygen limited.
\[ \boxed{\text{(C) The culture growth becomes oxygen limited}} \]