Question

A single bacterium is actively growing in a medium that supports its growth up to $100$ million. Assuming the division time of the bacterium as $3$ hours and the life span of non-dividing bacteria as $5$hours, which one of the following represents the maximum number of bacteria that would be present at the end of $15$ hours?

• A. $10$
• B. $64$
• C. $24$
• D. $32$

Answer 1

The correct option is D $32$

In the given problem, the medium supports the growth of up to 100 million bacteria. It means, till the population reaches 100 million, bacteria will keep on dividing and there will be no non-dividing bacteria. Generation time of the bacteria is 3 hours. It means, it takes 3 hours to divide. At the end of 15 hours, there will be total 5 generation time.

Number of bacteria at the end = 2${}^n$ where n is number of generation time.

Hence, number of bacteria present at the end of 15 hours = 2${}^5$ = 2 x 2 x 2 x 2 x 2 = 32.

Thus, the correct answer is option D.