Limitations of the exponential growth model: which choice correctly captures the model’s shortcomings in real cultures?

Introduction / Context:
The exponential growth model assumes constant specific growth rate and unlimited resources. While mathematically convenient, it is applicable only over a restricted interval in real bioprocesses. Recognizing its limitations helps motivate logistic, Monod-based, or structured models.

Given Data / Assumptions:

• Batch culture with finite nutrients and accumulating by-products.
• Exponential model: X(t) = X0 * e^(mu * t) with mu constant.
• Question focuses on limitations, not strengths.

Concept / Approach:
Real systems depart from constant-mu behavior as soon as substrate becomes limiting, oxygen transfer caps, pH drifts, or inhibitors accumulate. The exponential model does not incorporate any of these constraints. It is a local approximation during the log phase and cannot predict onset of stationary or death phases.

Step-by-Step Solution:
1) Evaluate option A: true—model applies during log phase only.2) Evaluate option B: true—model neglects slowing factors (resource and inhibition effects).3) Evaluate option C: false—exponential is not linear; it is exponential in time.4) Therefore, the best single choice summarizing the limitations is Both (a) and (b).

Verification / Alternative check:
Fitting exponential to early data works, but parameters drift as conditions change. Logistic or Monod models capture saturation or resource limitation better.

Why Other Options Are Wrong:
Option C contradicts the definition of the exponential model.Option D is correct; hence choices A or B alone are incomplete.

Common Pitfalls:
Believing exponential applies until nutrients are exhausted; in practice, mu declines earlier due to oxygen transfer, pH, and toxic by-products.

Final Answer:
Both (a) and (b)