Zipf's Law, developed by George Zipf in 1949, states that in a given country, the population of a city is inversely proportional to the city's rank by size in the country.116 Assuming Zipf's 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.

Question

Zipf's Law, developed by George Zipf in 1949, states that in a given country, the population of a city is inversely proportional to the city's rank by size in the country.116 Assuming Zipf's 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.

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