A bacterium divides every 35 minutes. If a culture containing 105 &#x

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?

Options:

A . 175 x 105 cells

B . 32 X 105 cells

C . 5 x 105 cells

D . 35 x 105 cells

Answer: Option B
:
B
The time taken by a bacterium to divide is calledgeneration time (G) or doubling time,since each parent cell divides into two daughter cells.
In this particular culture, the doubling time is 35 minutes. We are asked what will be cell concentration after 175 min.
Given,thegeneration time Gis 35 min.The total time elapsed (t)=175 min.
Then the cells would have divided or doubled 5 times (175/35=5), in this period. This means n=5 (wheren is the number of generations).
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.
This gives a simple formula= 2ⁿ. Given that n=5, then 2⁵=32.
This calculation, assumes that the starting culture contained a single cell.
In the problem, we are informed that the culture contained an initial cell concentration of 10⁵cells/mL.
Therefore, the final cell concentration after 175 min should be 10⁵X 32 cells/mL.

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