Zipfs Law, developed by George Zipf in 1949, states that in a given country, the

Chapter 1, Problem 26

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Zipfs Law, developed by George Zipf in 1949, states that in a given country, the population of a city is inversely proportional to the citys rank by size in the country.89 Assuming Zipfs Law: (a) Write a formula for the population, P, of a city as a function of its rank, R. (b) If the constant of proportionality k is 300,000, what is the approximate population of the largest city (rank 1)? The second largest city (rank 2)? The third largest city? (c) Answer the questions of part (b) if k = 6 million. (d) Interpret the meaning of the constant of proportionality k in this context. 2

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