Question

The specific growth rate of a mold is 0.15 h\(^{-1}\). If the cell concentration at 30 h is 33 g L\(^{-1}\), the concentration at 24 h (rounded to nearest integer) is \(\underline{\hspace{1cm}}\).

Hint:

Backward calculation in exponential growth uses negative exponent.

Answer 1

Correct Answer: 13

Exponential growth:
\[ X = X_0 e^{\mu t} \] Given:
\[ X(30) = 33,\ \mu = 0.15,\ \Delta t = 6\ \text{h} \] \[ X(24) = X(30)e^{-\mu(30-24)} = 33 e^{-0.9} \] \[ e^{-0.9} \approx 0.406 \] \[ X(24) = 33 \times 0.406 \approx 13.4 \] Rounded: 13–14 g/L