If a pathogen has a doubling time of 30 minutes, how many bacteria will be prese

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Question: If a pathogen has a doubling time of 30 minutes, how many bacteria will be present after 3 hours starting from a single bacterium?

Options:

Correct Answer: 64

Solution:

In 3 hours (180 minutes), there are 6 doubling periods (180/30). Starting from 1 bacterium, after 6 doublings, there will be 2^6 = 64 bacteria.

If a pathogen has a doubling time of 30 minutes, how many bacteria will be present after 3 hours starting from a single bacterium?

If a pathogen has a doubling time of 30 minutes, how many bacteria will be present after 3 hours starting from a single bacterium?

Correct Answer: 64

Step 1: Understand that the pathogen doubles every 30 minutes.
Step 2: Convert 3 hours into minutes. 3 hours is equal to 180 minutes.
Step 3: Calculate how many 30-minute periods are in 180 minutes. Divide 180 by 30, which equals 6.
Step 4: Start with 1 bacterium. Each doubling period means the number of bacteria multiplies by 2.
Step 5: After 1 doubling, there are 2 bacteria. After 2 doublings, there are 4 bacteria. After 3 doublings, there are 8 bacteria. After 4 doublings, there are 16 bacteria. After 5 doublings, there are 32 bacteria. After 6 doublings, there are 64 bacteria.
Step 6: Alternatively, you can use the formula 2^n, where n is the number of doublings. Here, n is 6, so 2^6 equals 64.

Exponential Growth – Understanding how bacteria multiply exponentially over time based on a given doubling time.
Doubling Time Calculation – Calculating the number of doubling periods within a specified time frame.
Power of Two – Applying the concept of powers of two to determine the final quantity after multiple doublings.