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

Options

A. 128
B. 24
C. 64
D. 32

Explanation

To solve the problem of how many protozoans will be in the population after six generations of binary fission, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Binary Fission**:
- Binary fission is a method of asexual reproduction where a single organism divides into two identical daughter cells. This process can be repeated in subsequent generations.

2. **Identify the Growth Pattern**:
- The growth of the population follows a geometric pattern. In each generation, every protozoan divides into two, effectively doubling the population.

3. **Determine the Formula**:
- The number of protozoans after 'n' generations can be calculated using the formula:
\[ \text{Population} = 2^n \]
- Here, 'n' is the number of generations.

4. **Substitute the Value of n**:
- In this case, we are asked to find the population after 6 generations. Therefore, we substitute \( n = 6 \) into the formula:
\[ \text{Population} = 2^6 \]

5. **Calculate the Population**:
- Now, calculate \( 2^6 \):
\[ 2^6 = 64 \]
- This means that after 6 generations, there will be 64 protozoans in the population.

### Final Answer:
After six generations of binary fission, the population of protozoans will be **64**.

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