State Board Nail Tech Practice Exam

How many additional bacteria can a single bacterium produce in half a day?

1. 1 million

2. 8 million

3. 16 million

4. 32 million

The correct answer is: 16 million

A single bacterium can reproduce through binary fission, a process in which one bacterium divides into two. This doubling occurs under optimal conditions, typically every 20 minutes. In half a day (which is 720 minutes or 36 cycles of 20 minutes), the initial bacterium can double multiple times. Starting with one bacterium, after each cycle of reproduction, the number of bacteria follows a "powers of two" pattern. Specifically, the formula for the number of bacteria after n divisions is given by 2^n, where n is the number of divisions. In this case, total divisions in half a day would be calculated as follows: 1 bacterium initially becomes 2 after the first cycle, 4 after the second, 8 after the third, and so forth. After 36 cycles, using 2 raised to the power of 36 gives the total number of bacteria produced. Calculating this, we find that 2^36 equals 68,719,476,736. Since the question relates to how many additional bacteria can be produced from the original single bacterium, this would be the total number of bacteria (68,719,476,736) minus the original one, resulting in 68