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Cell parameters - class-VIII
A cell weighing 1 mg grows to double its initial mass before dividing into two daughter cells of equal mass. Assuming no death, at the end of 100 divisions what will be the ratio of the mass of the entire populations of these cells to that of the mass of the Earth? Assume that mass of the Earth is $10^{24}Kg$ and $2^{10}$ is approximately equal to $1000$.
A cell starts at 1 mg (10^-6 kg) and divides 100 times. The total number of cells after 100 divisions is 2^100. The mass of the population is 10^-6 kg * 2^100. Given that 2^10 is approximately 10^3, 2^100 = (2^10)^10 is approximately (10^3)^10 = 10^30. Thus, total mass = 10^-6 kg * 10^30 = 10^24 kg, which matches the given mass of the Earth (10^24 kg). The ratio is therefore 1.