Final answer:
The correct calculation of population density after three hours of exponential growth starting at 100 CFU/ml and a bacteria dividing every 20 minutes would be 51200 CFU/ml. However, this result is not reflected in the provided multiple choice answers, suggesting an error in the question or answer choices.
Step-by-step explanation:
If you start out with a population density of 100 CFU/ml of a bacterium that divides every 20 minutes, the population density at the end of three hours can be determined using knowledge of bacterial growth rates during the log phase. Since one hour has three 20-minute intervals, in three hours there will be 9 divisions (20 minutes per division x 3 divisions per hour x 3 hours). To calculate the final population density, we apply the concept of exponential growth, using the formula 2n, where n represents the number of generations (or divisions). Here, n = 9, so the population will grow by 29 times.
29 = 512, and if we multiply this by the initial population density, we get the final population density: 512 x 100 CFU/ml = 51200 CFU/ml. However, from the options provided (A) 200 CFU/ml (B) 400 CFU/ml (C) 800 CFU/ml (D) 1600 CFU/ml, none match the calculated result. There may be an error in the question or the answer choices provided.