Question

A bacterium divides again every 35 minutes. If a culture containing ${10^5}$ cell per ml is grown for 175 minutes. What will be the cell concentration per ml after 175 mts __________.
A. \[32\: \times {10^5}\] cells
B. $5\: \times {10^5}$cells
C. $35\: \times {10^5}$cells
D. $175 \times {10^5}$cells

Answer 1

Hint: The number of divisions and the generation time of the bacterium calculate the number of cells in a culture at a defined time. If these values are known, then the number of cells in the culture can be calculated.

Complete answer:
Bacteria perform binary fission to carry out the process of cell division. A dividing bacterium copies the amount of DNA via replication. The cell membrane pinches inwards and forms a septum which is also known as the new dividing wall. The septum splits in the middle and two new cells are formed that live as an individual bacterium. According to the question, when a bacterium divides every 35 minutes and initially i.e. at zero minute, the culture contains about \[{10^5}\]cells/ml. Then, after 35 minutes, the culture contains about \[2\: \times {10^5}\] cells/ml. After 175 minutes, i.e. after five generations the culture contains about \[{2^5} \times {10^5}\]cells/ ml which is equal to\[32 \times {10^5}\]cells/ml.

Hence, the correct answer is option A.

Note: The exponential growth rate of a bacterial culture can be expressed as generation time or the doubling time. It can be expressed in the form of an equation- \[b = B \times {2^n}\]. Where, b is the number of bacteria at the beginning of cell division and B is the number of bacteria at the end of the cell division. N is the number of generations.