Q.A protozoan reproduces by binary fission. What will be the number of protozoans in its population after six generations?

In binary fission, one protozoan divides into two daughter cells. Each generation doubles the population. This is a geometric progression where the number after $n$ generations is $2^n$ times the starting number (assuming no deaths and all divisions are synchronous).

Starting from a single protozoan:

• After 1 generation: $2$
• After 2 generations: $4$
• After 3 generations: $8$
• After 4 generations: $16$ …

Binary fission is the most straightforward form of asexual reproduction seen in many protozoans, such as Amoeba and Paramecium. In this process, a single parent cell divides into two identical daughter cells. Each daughter cell is capable of growing and then dividing again. This means that every generation, the number of individuals doubles.

Think of it as a chain: start with one. After the first division, you have two. Those two each divide, giving four. Then four become eight, and so on. This pattern is a geometric progression where the population at any generation is given by $2^n$, where $n$ is the number of generations.

Now, the question asks for the number after six generations. Starting from one protozoan:

• Generation 1: 2
• Generation 2: 4
• Generation 3: 8 …

Write the sequence out generation by generation (1, 2, 4, 8, 16, 32, 64) instead of computing $2^6$ mentally -- it makes it unambiguous that 'after six generatio …