Q.56 The specific growth rate of a mold during exponential phase of its growth in a batch
cultivation is 0.15 h−1. If the cell concentration at 30 h is 33 g L−1,
the cell concentration in g L−1 (rounded off to the nearest integer) at 24 h is _________.
Calculate Mold Cell Concentration at 24 Hours in Exponential Growth
Mold exhibits exponential growth in batch cultivation with a specific growth rate (μ) of 0.15 h-1. Given a cell concentration (X) of 33 g L-1 at 30 hours, the concentration at 24 hours computes to 13 g L-1 using the exponential growth equation.
Exponential Growth Equation
Cell concentration follows Xt = X0eμt during exponential phase, where μ = 0.15 h-1. To find X24 from X30 = 33 g L-1 over Δt = 6 hours backward, rearrange as X24 = X30 × e-μΔt.
Step-by-Step Calculation
Compute exponent: μ Δt = 0.15 × 6 = 0.9, so e-0.9 ≈ 0.4066. Thus, X24 = 33 × 0.4066 ≈ 13.42 g L-1, rounded to 13.
Why This Approach Works
Exponential growth yields constant μ, enabling direct back-calculation without initial concentration. No lag or stationary phase assumptions apply here, as the problem specifies exponential phase.
Common Mistakes Explained
- Forgetting to use natural log base: Using 10-base or linear growth overestimates/underestimates by factors >2.
- Wrong time direction: Forward calculation from 24h to 30h gives ~81 g L-1, incorrect for backward query.
- Ignoring rounding: 13.42 rounds to 13 per instructions; 13.5+ would be 14.
This matches GATE bioprocess standards for microbial kinetics.
