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Bacteria grow by a given percent in 2 hours: time for the count to double

The same question, asked 2 times: 16 May 2023 S2*, 21 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S2

    134
    The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at t=0t=0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after klog⁡65\dfrac{k}{\log\frac{6}{5}} hours, then (klog⁡2)2\left(\dfrac{k}{\log 2}\right)^2 is

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  2. Question 2

    21 Apr 2025 S2

    150
    In a culture bacteria count is 1,00,0001,00,000 initially. The number increases by 10%10\% in first 2 hours. In how many hours will the count reach 2,00,0002,00,000, if the rate of growth of bacteria is proportional to the number present?

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