If a pathogen has a doubling time of 30 minutes, how many bacteria will be present after 3 hours starting from a single bacterium?
Practice Questions
1 question
Q1
If a pathogen has a doubling time of 30 minutes, how many bacteria will be present after 3 hours starting from a single bacterium?
8
16
32
64
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.
Questions & Step-by-step Solutions
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Q
Q: If a pathogen has a doubling time of 30 minutes, how many bacteria will be present after 3 hours starting from a single bacterium?
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.
Steps: 6
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.
