GATE 2021 BT – Question 32
A bacterial strain has decimal reduction time 20 min. Specific death rate constant (min⁻¹, two decimal places) is _______.
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Correct answer: 0.11 to 0.13
Explanation
The **decimal reduction time** $D$ is the time needed to kill 90% of the cells, i.e. to reduce the number by a factor of 10.
For first-order death $N=N_0e^{-k_dt}$:
$$\frac{N}{N_0}=\frac1{10}\;\Rightarrow\;k_dD=\ln10 .$$
**Numbers.**
$$k_d=\frac{\ln10}{D}=\frac{2.3026}{20\text{ min}}=0.1151\approx\mathbf{0.12\ min^{-1}}.$$