Question

Under ideal conditions, a bacterium can divide into two bacteria every 20 minutes. Then each of those can divide into new ones every twenty minutes if you start with one bacteria, how many bacterias will you have in one hour, two hours, five hours, and eight hours?

Answer 1

Under ideal conditions where a bacterium can divide every 20 minutes, after one hour you would have 8 bacteria. After two hours there would be 64 bacteria, after five hours 32,768 bacteria, and after eight hours, the population would reach 16,777,216 bacteria.

Step-by-step explanation:

Bacteria exhibit exponential growth, which is a type of growth wherein the population size doubles after every given time period. In the scenario provided, a single bacterium divides every 20 minutes. This means in the first hour (three 20-minute intervals), the number of bacteria will double three times:

• After the first 20 minutes: 1 x 2 = 2 bacteria
• After the second 20 minutes (40 min total): 2 x 2 = 4 bacteria
• After the third 20 minutes (60 min total): 4 x 2 = 8 bacteria

So, after one hour, there would be 8 bacteria.

Following this pattern:

• After two hours (6 doubling periods): 1 x 26 = 64 bacteria
• After five hours (15 doubling periods): 1 x 215 = 32,768 bacteria
• After eight hours (24 doubling periods): 1 x 224 = 16,777,216 bacteria

Each doubling time represents a complete cycle of binary fission, where one bacterium splits into two.