Question

A bacterium that arose 3.5 billion years ago divides once every 12 hours. Under ideal conditions, the number of generations the bacterium has undergone will be approximately:

• A. \( 2.6 \times 10^{12} \)
• B. \( 73 \times 10^9 \)
• C. \( 1.06 \times 10^{12} \)
• D. \( 1.3 \times 10^{12} \)

Hint:

To calculate bacterial generations over a long time span, consider the growth rate and time for each generation.

Answer 1

The Correct Option is A

Step 1: Understanding bacterial growth.
Bacterial growth follows exponential growth. The number of generations can be calculated using the formula: \[ N = N_0 \times 2^n \] where \( N_0 \) is the initial number of bacteria, \( n \) is the number of generations, and \( N \) is the final number of bacteria.

Step 2: Estimating the number of generations.
The bacterium divides every 12 hours, so in 3.5 billion years, the number of generations would be approximately: \[ n = \frac{3.5 \times 10^9 \text{ years} \times 365 \times 24 \text{ hours}}{12 \text{ hours}} \approx 1.06 \times 10^{12} \]

Step 3: Conclusion.
The correct answer is (C) because after 3.5 billion years, the bacterium will have undergone approximately \( 1.06 \times 10^{12} \) generations.