In a closed system, how many generations are required for a single bacterial cell to produce a population of 256 cells, assuming each generation results in a doubling of cell number?

• A. 8
• B. 16
• C. 128
• D. 256

Answer: (A)

Verified step by step guidance

1. Understand that each generation results in a doubling of the bacterial population. This means the population size after n generations can be expressed as \(N = N_0 \times 2^n\), where \(N_0\) is the initial number of cells and \(n\) is the number of generations.
2. Identify the initial population size \(N_0\). In this problem, it is given as a single bacterial cell, so \(N_0 = 1\).
3. Set the final population size \(N\) to 256 cells, as given in the problem.
4. Use the formula \(N = N_0 \times 2^n\) and substitute the known values: \$256 = 1 \times 2^n\(, which simplifies to \)256 = 2^n$.
5. Solve for \(n\) by taking the logarithm base 2 of both sides: \(n = \log_2(256)\). This will give the number of generations required to reach 256 cells.