Protozoan Population Growth by Binary Fission

Protozoans are single-celled organisms, and many of them reproduce asexually through a process called binary fission. Binary fission is a method of reproduction where a single cell divides into two identical daughter cells. This means that with each generation, the population of protozoans effectively doubles.

Let's start with an initial population of one protozoan and see how the number grows over eight generations:

• Starting Population (Generation 0): 1 protozoan
• After Generation 1: \(1 \times 2 = 2\) protozoans
• After Generation 2: \(2 \times 2 = 4\) protozoans
• After Generation 3: \(4 \times 2 = 8\) protozoans
• After Generation 4: \(8 \times 2 = 16\) protozoans
• After Generation 5: \(16 \times 2 = 32\) protozoans
• After Generation 6: \(32 \times 2 = 64\) protozoans
• After Generation 7: \(64 \times 2 = 128\) protozoans
• After Generation 8: \(128 \times 2 = 256\) protozoans

Alternatively, we can think of this as exponential growth. If we start with 1 protozoan, after \(n\) generations of binary fission, the number of protozoans will be \(1 \times 2^n\).

In this question, we are looking for the population after eight generations, so \(n=8\).

Number of protozoans = \(1 \times 2^8\)

Now we calculate \(2^8\):

\(2^1 = 2\)
\(2^2 = 4\)
\(2^3 = 8\)
\(2^4 = 16\)
\(2^5 = 32\)
\(2^6 = 64\)
\(2^7 = 128\)
\(2^8 = 256\)

So, after eight generations, the number of protozoans will be 256.

This growth pattern demonstrates the power of exponential increase through binary fission.