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Math Help - 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.

     n \propto \frac{1}{S} \Rightarrow n = \frac{k}{S}<br />

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

     n = \frac{k}{S}

     48 = \frac{k}{350000}

     k = 16800000 Therefore

     n = \frac{16800000}{S}

    now you require S > 200000 so

     n = \frac{16800000}{S}

     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 N=\frac{k}{S}. So we have 48=\frac{k}{350000} and from this we can calculate k. Then we use 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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