​Ten bacterial cells are inoculated into 10 ml of Luria broth and grown for 10 hours with shaking at 37°C. What will be the approximate number of bacteria in the flask at the end of 10-hour incubation? (Note: the doubling time of this bacterium in Luria broth is approximately 20 min).​

Correct option is D

The correct option is (d)

To calculate the approximate number of bacteria after 10 hours, we use the concept of exponential growth where the bacterial population doubles every doubling time.

Step 1: Determine the number of doubling periods in 10 hours.
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Doubling time = 20 minutes
Total incubation time = 10 hours = 10 × 60 = 600 minutes
Number of doublings = Total time / Doubling time = 600 / 20 = 30 doublings

Step 2: Use the formula for exponential growth:

$$N = N_0 \times 2^n$$

where, 

​$$N_0 = \text{initial number of bacteria} = 10$$

$$n = \text{number of doublings} = 30$$

$$\bullet \quad N = \text{number of bacteria after 30 doublings}$$

Step 3 : Calculate the final population:

​$$N = 10 \times 2^{30} = 10 \times 1,073,741,824 \approx 1.07 \times 10^{10}$$

Hence the approximate number of bacteria is close to 10¹⁰
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