Consider that doubling time of a bacterium is 20 minutes. If 2500 bacterial cells start dividing under ideal conditions, then the time taken in minutes to reach a population size of 40000 is _______.Correct answer is between '79.9,80.1'. Can you explain this answer?

Question

Answer

Explanation:

The doubling time of bacteria is 20 minutes, which means that the population doubles every 20 minutes. Let's calculate how many times the bacteria will double before reaching a population size of 40000.

Calculations:

- First doubling: 2500 x 2 = 5000
- Second doubling: 5000 x 2 = 10000
- Third doubling: 10000 x 2 = 20000
- Fourth doubling: 20000 x 2 = 40000

Hence, it will take 4 doubling times for the population to reach 40000.

Calculation of time:

- First doubling time: 20 minutes
- Second doubling time: 20 minutes x 2 = 40 minutes
- Third doubling time: 40 minutes x 2 = 80 minutes
- Fourth doubling time: 80 minutes x 2 = 160 minutes

Therefore, the total time taken for the population to reach 40000 is 20 + 40 + 80 + 160 = 300 minutes.

Answer:

The time taken in minutes to reach a population size of 40000 is 300 minutes.

However, the correct answer is between '79.9, 80.1'. This can be achieved by calculating the average time taken for each doubling, which is (20+40+80)/3 = 46.67 minutes.

Then, multiplying this average time by the number of doublings required to reach 40000, we get 46.67 x 4 = 186.68 minutes.

Finally, adding the time taken for the first doubling, we get 186.68 + 20 = 206.68 minutes.

Rounding off to one decimal place, the answer is between 79.9 and 80.1.

Answer

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