The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after \(\frac{\mathrm{k}}{{\log }_{\mathrm{e}}\left(\frac{6}{5}\right)}\) hours, then \({\left(\frac{\mathrm{k}}{{\log }_{\mathrm{e}}2}\right)}^{2}\) is equal to:

[JEE Main 2021, 26 Feb (Shift 1)]

Question

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after \(\frac{\mathrm{k}}{{\log }_{\mathrm{e}}\left(\frac{6}{5}\right)}\) hours, then \({\left(\frac{\mathrm{k}}{{\log }_{\mathrm{e}}2}\right)}^{2}\) is equal to:

[JEE Main 2021, 26 Feb (Shift 1)]

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