USA Biology Olympiad (USABO) Practice Exam

How much time is estimated for a population of type A cells to increase by 300 percent, given a generation time of 28 minutes?

1. Approximately 28 minutes

2. Approximately 42 minutes

3. Approximately 56 minutes

4. Approximately 70 minutes

The correct answer is: Approximately 42 minutes

To determine how much time is required for a population of type A cells to increase by 300 percent, we first need to understand what a 300 percent increase means in terms of the original population. An increase of 300 percent indicates that the final population will be four times the initial population (the original plus three times the original). When considering the growth of a population with a specific generation time, we can use the formula for exponential growth, which states that after one generation, the population doubles. In this case, with a generation time of 28 minutes, the population will grow as follows: - At 0 generations (initial population): 1x - At 1 generation (28 minutes later): 2x - At 2 generations (56 minutes later): 4x Since a 300 percent increase leads us to a final population of 4 times the initial (from 1x to 4x), we realize that this takes exactly 2 generations. Each generation takes 28 minutes, so multiplying the number of generations by the generation time gives us: 2 generations × 28 minutes/generation = 56 minutes. Thus, the estimated time for a population of type A cells to increase by 300 percent