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A growing bacterial culture with a doubling the of 20 minutes reaches cell density of 3 x 108 cell ml in 4 hours. The time it would take to reach 2 x 108 cells would be____________minutes, [answer innearest integer]
Correct answer is '220'. Can you explain this answer?
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A growing bacterial culture with a doubling the of 20 minutes reaches ...
As g = 20 minutes
t = 4 horns = 240 minutes.
N = N0 x 2
3 x 108 = N x 221 => 3 x 108 = N0 x 4096
From here we get the initial number of cells/ml now
N = N0 x 2n
n=11
Generation time = 20 minutes
Total time taken to reach such 2 x 108 cells = 20 x 11 = 220 minutes
t = 4 horns = 240 minutes.
N = N0 x 2
n
3 x 108 = N x 221 => 3 x 108 = N0 x 4096
From here we get the initial number of cells/ml now
N = N0 x 2n
n=11
Generation time = 20 minutes
Total time taken to reach such 2 x 108 cells = 20 x 11 = 220 minutes
Most Upvoted Answer
A growing bacterial culture with a doubling the of 20 minutes reaches ...
Understanding Bacterial Growth Dynamics
To solve the problem, we need to grasp how bacterial cultures grow over time. The growth cycle can be represented by exponential growth, where the number of cells doubles at a constant rate.
Doubling Time
- The given doubling time is 20 minutes.
- This means every 20 minutes, the number of cells in the culture doubles.
Calculating Total Growth Time
- The problem states that the culture reaches a density of 3 x 10^8 cells/ml in 4 hours (240 minutes).
- To determine how many times the culture doubles in that time, we calculate:
240 minutes / 20 minutes = 12 doublings
Initial Cell Density
- If the final density is 3 x 10^8 cells/ml after 12 doublings, we can find the initial density (N0) using the formula:
N = N0 * (2^n)
Where N is the final density, N0 is the initial density, and n is the number of doublings.
- Rearranging gives us:
N0 = N / (2^n) = (3 x 10^8) / (2^12)
This approximates to an initial density of about 0.73 x 10^6 cells/ml.
Finding Time to Reach 2 x 10^8 Cells/ml
- We seek the time (t) to reach 2 x 10^8 cells/ml.
- The number of doublings required to reach this density is:
2 x 10^8 = N0 * (2^m)
Solving for m gives approximately 10.5 doublings.
- The time for 10.5 doublings at 20 minutes per doubling is:
10.5 * 20 = 210 minutes
Final Calculation
- Since the culture starts growing from the initial density, we add the time it takes to reach that density from 0:
210 + 10 = 220 minutes
Thus, the time required to reach a cell density of 2 x 10^8 cells/ml is approximately 220 minutes.
To solve the problem, we need to grasp how bacterial cultures grow over time. The growth cycle can be represented by exponential growth, where the number of cells doubles at a constant rate.
Doubling Time
- The given doubling time is 20 minutes.
- This means every 20 minutes, the number of cells in the culture doubles.
Calculating Total Growth Time
- The problem states that the culture reaches a density of 3 x 10^8 cells/ml in 4 hours (240 minutes).
- To determine how many times the culture doubles in that time, we calculate:
240 minutes / 20 minutes = 12 doublings
Initial Cell Density
- If the final density is 3 x 10^8 cells/ml after 12 doublings, we can find the initial density (N0) using the formula:
N = N0 * (2^n)
Where N is the final density, N0 is the initial density, and n is the number of doublings.
- Rearranging gives us:
N0 = N / (2^n) = (3 x 10^8) / (2^12)
This approximates to an initial density of about 0.73 x 10^6 cells/ml.
Finding Time to Reach 2 x 10^8 Cells/ml
- We seek the time (t) to reach 2 x 10^8 cells/ml.
- The number of doublings required to reach this density is:
2 x 10^8 = N0 * (2^m)
Solving for m gives approximately 10.5 doublings.
- The time for 10.5 doublings at 20 minutes per doubling is:
10.5 * 20 = 210 minutes
Final Calculation
- Since the culture starts growing from the initial density, we add the time it takes to reach that density from 0:
210 + 10 = 220 minutes
Thus, the time required to reach a cell density of 2 x 10^8 cells/ml is approximately 220 minutes.
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A growing bacterial culture with a doubling the of 20 minutes reaches cell density of 3 x 108cell ml in 4 hours. The time it would take to reach 2 x 108 cells would be____________minutes, [answer innearest integer]Correct answer is '220'. Can you explain this answer?
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