USA Biology Olympiad (USABO) Practice Exam

During the logarithmic phase of bacterial growth, what formula relates the total number of cells to the original number?

1. b = (B)(2n)

2. b = (B)(2g)

3. b = (B)(n)

4. b = (B + 2n)

The correct answer is: b = (B)(2n)

The correct relationship during the logarithmic phase of bacterial growth is indeed represented by the formula b = (B)(2^n). In this context, "b" refers to the total number of cells after a certain period, "B" is the original number of cells, and "n" represents the number of generations that have occurred. During the logarithmic or exponential phase of growth, bacteria divide at a constant rate. The formula indicates that for each generation (n), the number of cells doubles. Thus, after n generations, the total number of cells can be calculated by multiplying the original number of cells (B) by 2 raised to the power of the number of divisions (n), which reflects the exponential nature of bacterial growth. This model is crucial because it accurately depicts the behavior of bacterial populations in ideal conditions, where resources are abundant, and environmental factors are conducive to rapid growth. Understanding this formula helps in applications like calculating bacterial population densities in microbiology and predicting growth rates in biotechnological processes.