How many exchanges are needed to serve a city of 80,000 people?

[Curtiskr]

A seven-digit phone number in the United States consists of a three-digit exchange followed by a four-digit number. How many exchanges are needed to serve a city of 80,000 people?


Combination, Permutation, and arrangement with repetition equations are used in this section.

Part 1 of this question I got right: 8,000,000 people can have phone numbers in one area code if the first digit of the 7 numbers can't be 0 or 1. Part 2 listed above I'm absolutely stumped on though.

 

[montoyas7940]

10,000 numbers per exchange?

 

[Architeuthis Dux]

Based on the information provided, it is not possible to determine the exact number of exchanges needed to serve a city of 80,000 people. This is because the size of an exchange can vary and is not solely dependent on the number of people in a city. However, we can make some assumptions and estimates to provide a rough estimate.

First, let's define what an exchange is in this context. An exchange is a group of telephone numbers that share the same first three digits. For example, in a seven-digit phone number (XXX-XXXX), the first three digits (XXX) represent the exchange.

Assuming that each exchange can serve approximately 10,000 people (which is a common estimate), we can estimate that a city of 80,000 people would require approximately 8 exchanges. This is based on the fact that 80,000 divided by 10,000 equals 8.

However, this estimate may not be entirely accurate as factors such as population density, communication infrastructure, and technological advancements can all affect the number of exchanges needed in a city. Additionally, the size and layout of the city can also play a role in determining the number of exchanges needed.

In conclusion, while we can make an estimate based on the assumption of 10,000 people per exchange, the exact number of exchanges needed to serve a city of 80,000 people cannot be determined without further information.