Question

Biology

Posted 5 months ago

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The bacterium Bacillus symbiodinium has a generation time of 20 minutes. Starting with one cell in log phase, how many minutes does it take to produce about 1,000 cells $(2 n=1000)$ ? Assume all cells remain viable
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Answer from Sia

Posted 5 months ago

Answer

It takes 200 minutes to produce about 1,000 cells from one cell of Bacillus symbiodinium.

Solution

a

Determine the number of generations required to reach 1,000 cells: Use the formula $2^n = 1000$ to find n

b

Calculate the number of generations: Solving for n gives $n = \log_2{1000} \approx 9.97$. Since we cannot have a fraction of a generation, we round up to 10 generations

c

Calculate the total time: Multiply the number of generations by the generation time. For Bacillus symbiodinium, the generation time is 20 minutes, so $10 \times 20 = 200$ minutes

Key Concept

Generation time and exponential growth

Explanation

The generation time is the time it takes for a population to double. Bacterial growth can be modeled exponentially, and the time to reach a certain population size can be calculated by determining the number of generations required and multiplying by the generation time.

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