GATE 2021 BT – Question 56
A mold grows exponentially at 0.15 h⁻¹. Its concentration at 30 h is 33 g/L. Concentration at 24 h (nearest integer g/L) is _______.
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Correct answer: 13
Explanation
For exponential growth, $X=X_0e^{\mu t}$, so the concentration at two times is related by
$$X(t_2)=X(t_1)\,e^{\mu(t_2-t_1)} .$$
**Going back 6 hours** from 30 h to 24 h:
$$X_{24}=X_{30}\,e^{-\mu\times6}=33\,e^{-0.15\times6}=33\,e^{-0.9}=33\times0.4066=13.4 .$$
The concentration at 24 h is **13 g/L** (to the nearest integer).