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Notes

Questions

\(\textbf{1)}\) There are 400,000 people living within a 5 miles radius of thecity center of Sometown, USA. What is the population density?

Show Answer

The population density is \(\approx 5{,}093\) people per square mile

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{People}}{\text{Area }(\pi r^2)}\)

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{400{,}000}{\pi(5)^2}\)

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{16{,}000}{\pi}\approx 5{,}093\)

\(\textbf{2)}\) Within 4 miles of city center of KarenVille, the population density is 500 people per square mile. What is the population of KarenVille?

Show Answer

The population is \(\approx 25,133\) people

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }(\pi r^2)}\)

\(\,\,\,\,\,500=\displaystyle\frac{x}{\pi(4)^2}\)

\(\,\,\,\,\,\displaystyle\frac{500}{1}=\displaystyle\frac{x}{16\pi}\)

\(\,\,\,\,\,x=8{,}000\pi\approx 25{,}133\)

\(\textbf{3)}\) 540 people live in a 10 acre town. What is the population density of the town?

Show Answer

The population density is \( 54 \) people per acre

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{540 \text{ people}}{10 \text{ acres}}\)

\(\,\,\,\,\,\text{Population Density}=54 \frac{\text{people}}{\text{acre}}\)

\(\textbf{4)}\) 78,000 people live in a town with population density of 500 people per square mile. What is the total area of the town?

Show Answer

The total area of the town is \( 156 \) square miles

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,500=\displaystyle\frac{78{,}000}{x}\)

\(\,\,\,\,\,500x=78{,}000\)

\(\,\,\,\,\,x=156\)

\(\textbf{5)}\) The population density of a rural area is 20 people per square kilometer. If the area of the rural region is 500 square kilometers, what is the total population of the area?

Show Answer

The total population is \( 10,000 \) people

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,20=\displaystyle\frac{x}{500}\)

\(\,\,\,\,\,x=20 \times 500 = 10,000\)

\(\textbf{6)}\) If a city has a population of 200,000 and a population density of 800 people per square kilometer, what is the area of the city in square kilometers?

Show Answer

The area of the city is \( 250 \) square kilometers

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,800=\displaystyle\frac{200{,}000}{x}\)

\(\,\,\,\,\,800x=200{,}000\)

\(\,\,\,\,\,x=250\)

\(\textbf{7)}\) In a suburban area, there are 15,000 people residing in a 5 square mile region. What is the population density of the suburban area?

Show Answer

The population density is \( 3,000 \) people per square mile

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{15{,}000}{5}=3{,}000\)

\(\textbf{8)}\) A village has a population density of 100 people per square kilometer. If the population of the village is 2,500, what is the area of the village in square kilometers?

Show Answer

The area of the village is \( 25 \) square kilometers

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,100=\displaystyle\frac{2{,}500}{x}\)

\(\,\,\,\,\,100x=2{,}500\)

\(\,\,\,\,\,x=25\)

\(\textbf{9)}\) If a town has a population of 80,000 and a population density of 200 people per square kilometer, what is the area of the town in square kilometers?

Show Answer

The area of the town is \( 400 \) square kilometers

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,200=\displaystyle\frac{80{,}000}{x}\)

\(\,\,\,\,\,200x=80{,}000\)

\(\,\,\,\,\,x=400\)

\(\textbf{10)}\) A forest reserve has a population density of 5 animals per square kilometer. If the reserve covers an area of 1,000 square kilometers, what is the total animal population in the reserve?

Show Answer

The total animal population is \( 5,000 \)

Show Work

\(\,\,\,\,\,\text{Population Density}=\displaystyle\frac{\text{Population}}{\text{Area }}\)

\(\,\,\,\,\,5=\displaystyle\frac{x}{1{,}000}\)

\(\,\,\,\,\,x=5 \times 1{,}000 = 5{,}000\)

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In Summary

Population density is a measure of how many people live in a particular area. It is typically expressed as the number of people per square kilometer or square mile. We learn about population density in order to understand how people are distributed across the globe. This information can help us make informed decisions about things like resource allocation, infrastructure development, and social services.

A fun fact about population density is that the most densely populated country in the world is Monaco, with a population density of over 16,000 people per square kilometer.

The concept of population density was first introduced by Thomas Malthus in his work “An Essay on the Principle of Population,” published in 1798. Malthus used population density as a way to understand the potential for population growth and its impact on resource availability.

Some related topics to population density include population growth, urbanization, and demographics. Understanding population density can help us better understand these other concepts and how they impact society and the environment.

Topics that use Population Density

Demographics: Population density is an important concept in the study of demographics, as it helps us understand how people are distributed across different regions and how population patterns are changing over time.

Statistics: Population density is often used in statistical analysis to compare different regions or countries. It can be used to calculate the mean, median, or mode of a population, or to compare the distribution of populations across different areas.

Geography: Population density is an important concept in geography, as it helps us understand how people are distributed across the earth’s surface. It is often used to compare different regions or to study the impact of population density on things like resource availability and infrastructure development.

Economics: Population density can have an impact on economic factors such as resource availability and labor markets. It is often used to study the economic impact of population growth and change.

Environmental science: Population density can have an impact on the environment, as a higher population density can lead to more resource consumption and waste production. It is often used to study the environmental impact of population growth and change.

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