In a batch reactor, how does the specific growth rate μ typically behave over the course of the fermentation (from lag through stationary phases)?

Introduction / Context:
Batch cultures are closed systems: nutrients deplete, products accumulate, and pH or dissolved oxygen can drift. The specific growth rate μ therefore varies across lag, exponential, deceleration, and stationary phases. This question tests the basic temporal profile of μ in batch operation.

Given Data / Assumptions:

• No feed or bleed; volume is constant (ignoring evaporation, gas exchange).
• Substrate and oxygen are finite; products and acids/ethanol may accumulate.
• Physiology adapts from inoculation to stationary phase.

Concept / Approach:
In lag, μ ≈ 0 while cells adapt. In exponential phase, μ ≈ μ_max if nutrients and O2 are abundant. As limitations and inhibition set in, μ declines. Finally, in stationary phase, net μ approaches 0 as growth balances death or ceases due to depletion/stress.

Step-by-Step Solution:

Verification / Alternative check:
Typical growth curves of OD or dry cell weight show sigmoidal behavior consistent with changing μ.

Why Other Options Are Wrong:

• Constant μ: only holds during a portion of exponential growth.
• Unbounded exponential: violates resource limits.
• Highest in stationary: contradictory by definition.
• Instant drop to zero after inoculation: ignores exponential phase.

Common Pitfalls:
Assuming a single μ fits the whole batch when modeling long runs.

Final Answer:
It changes during the fermentation as conditions evolve.