Final answer:
The bacteria in question exhibit exponential growth, doubling in population every 20 minutes. Using the formula for exponential growth (200 * 2^n), where n is the number of intervals, we can calculate the total number of bacteria cells after 2 hours to be 12,800.
Step-by-step explanation:
The subject of the question pertains to exponential growth, which is a concept covered in mathematics, specifically in the areas of algebra and functions. Exponential growth is often represented in real-life scenarios like population growth, which is a common theme in biology. However, this is a mathematical calculation and thus categorized under mathematics. The question asks for the number of bacteria after a certain time period, given their exponential growth rate.
The initial population of bacteria is 200, and we are told that the population doubles every 20 minutes. To find the total number of bacteria after 2 hours (which is equal to 120 minutes), we first need to determine how many 20-minute intervals there are in 2 hours. This is calculated by dividing 120 by 20, which results in 6 intervals.
The number of bacteria after each interval can be represented as the initial amount multiplied by 2 raised to the power of the number of intervals (2n, with n being the number of intervals). Thus, after 2 hours, the number of bacteria cells will be 200 * 26, which equates to 200 * 64 = 12,800 cells.