If an infection starts with a single bacterium that undergoes binary fission every hour, how many bacteria will there be after 5 hours?
The correct answer and explanation is:
The correct answer is 32 bacteria after 5 hours.
Explanation:
Binary fission is the process by which bacteria reproduce asexually. In this process, one bacterium divides into two identical daughter cells. This doubling occurs at regular time intervals, in this case, every hour.
Starting with a single bacterium, the number of bacteria doubles each hour. The growth can be described by the formula: N=N0×2tN = N_0 \times 2^t
where:
- NN is the number of bacteria after time tt,
- N0N_0 is the initial number of bacteria,
- tt is the number of hours (or number of division cycles).
Given:
- Initial number of bacteria, N0=1N_0 = 1,
- Division time = 1 hour,
- Total time, t=5t = 5 hours.
Applying the formula: N=1×25=25=32N = 1 \times 2^5 = 2^5 = 32
This means after 5 hours, there will be 32 bacteria.
The exponential growth here shows how quickly bacteria populations can increase under ideal conditions. Each hour, the population doubles, leading to rapid expansion from a single cell to a large group. This doubling pattern is fundamental in microbiology for understanding bacterial cultures, infections, and even food spoilage.
In real-world scenarios, factors such as nutrient availability, space, temperature, and immune system responses can affect bacterial growth and prevent this ideal doubling rate from continuing indefinitely. However, under laboratory or ideal conditions, the doubling time remains a critical parameter in calculating population growth.
Understanding this exponential growth is important for predicting infection spread and timing antibiotic treatments. It also demonstrates why early detection and control of bacterial infections are crucial since a small number of bacteria can quickly become a large population capable of overwhelming defenses.