GATE 2022 BT – Question 65
An aerobic bacterial culture at 37°C starts with $10^2$ cells and reaches $10^5$ after 10 h. The doubling time (nearest integer h) is ___________.
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Correct answer: 1
Explanation
In exponential growth the number of cells doubles every doubling time, so
$$N=N_0\cdot2^{\,t/t_d}\;\Rightarrow\;t_d=\frac{t\ln2}{\ln(N/N_0)} .$$
**Numbers.** $N_0=10^2$, $N=10^5$, $t=10$ h. The cells increase by a factor of $10^3$:
$$\ln(10^3)=6.908,\qquad t_d=\frac{10\times0.693}{6.908}=1.003\text{ h}.$$
The doubling time is **1 h** (about 9.97 generations in 10 h).