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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