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Thread: problem solving

  1. #1
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    Post problem solving

    According to Zipf's Law, the number of cities with a population greater than S is inversely proportional to S. In 2000, there were 48 US cities with a population greater than 350,000. estimate the number of US cities with a population greater than 200,000.

    Any help..! I would really appreciate it.!
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  2. #2
    Master Of Puppets
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    I think the following maybe helpful.

    $\displaystyle n \propto \frac{1}{S} \Rightarrow n = \frac{k}{S}
    $

    Using $\displaystyle (S,n) = (350000,48)$ we can find k.

    $\displaystyle n = \frac{k}{S}$

    $\displaystyle 48 = \frac{k}{350000}$

    $\displaystyle k = 16800000$ Therefore

    $\displaystyle n = \frac{16800000}{S}$

    now you require $\displaystyle S > 200000$ so

    $\displaystyle n = \frac{16800000}{S}$

    $\displaystyle n = \frac{16800000}{200000}$

    Can you finish it from here?
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  3. #3
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    "number N of cities with a population greater than S is inversely proportional to S" means that there exists a non-zero constant k such that $\displaystyle N=\frac{k}{S}$. So we have $\displaystyle 48=\frac{k}{350000}$ and from this we can calculate k. Then we use $\displaystyle N=\frac{k}{S}$ again, with k we just calculated, to obtain the number of US cities with a population greater than 200,000.
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  4. #4
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    Re: problem solving

    Thanks so much for the info!! =))
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