1. 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.!

2. 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?

3. "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.

4. Re: problem solving

Thanks so much for the info!! =))