Question

A bacterium divides every 35 minutes. If a culture containing 10⁵ cells per mL is grown for 175 min, what will be the cell concentration per mL after 175 minutes?

32 X 10⁵ cells

175 x 10⁵ cells

5 x 10⁵ cells

35 x 10⁵ cells

• A. 175 x 10⁵ cells
• B. 32 X 10⁵ cells
• C. 5 x 10⁵ cells
• D. 35 x 10⁵ cells

Answer 1

The correct option is A

Explanation of the correct option

1. The time taken by a bacterium to divide is called generation time (G) or doubling time since each parent cell divides into two daughter cells.
2. In this particular culture, the doubling time is 35 minutes. We are asked what the will be cell concentration after 175 min.
3. Given, the generation time G is 35 min. The total time elapsed (t)= 175 min.
4. Then the cells would have divided or doubled 5 times (175/35=5), in this period. This means n=5 (where n is the number of generations).
5. After one doubling, a single cell would become 2 cells. In the second generation, these 2 cells would double to 4 cells, and so on.
6. This gives a simple formula= 2n. Given that n=5, then 25=32.
7. This calculation assumes that the starting culture contained a single cell.
8. In the problem, we are informed that the culture contained an initial cell concentration of 105 cells/mL.

Final Answer: the final cell concentration after 175 min should be 10⁵ X 32 cells/mL.