ANSWER KEY
Population Math Concepts & Equations You Should Memorize:
Population Density = (Population)
(AREA)
For example: (2,700,000 people) = 29 people per square km
(9,166,605 sq km)
Birth or Death Rates = (# of births/deaths per year)
(Total population)
For example: (23,452 births) = 0.025 = 2.5% birth rate
(942,271 people)
Finding Population Growth Rate (r):
r = (births – death)
Note: This does not include immigration/emigration. If it did, it would be (b + e) – (i + d)
(total population)
total population
For example: (20,000 births – 15,000 deaths) = 0.01 = 1.0%
(500,000 people)
Doubling Time = THE RULE OF 70
(70%)
r (in percent form)
or
(0.7)
r (in decimal form)
Finding Future Population from Growth Rate…
(initial population) x (growth rate) years = Final Population
NOTE: a growth rate of 3% is expressed as 1.03; a growth rate of 0.25% is 1.0025
for example: (468,843 people ) X ( 1.03 )10 years = 630,085 people
All answers are approximate – when you aren’t using a calculator you have a little liberty to round!
1. At the end of 2002, there were 1,284.53 million people living in China. China is the third largest country in the
world with an area of 9.6 million square kilometers. What is the population density of China?
Population Density = (Population) = 1284.53 = 134 people per sq km
(AREA)
9.6
2. China has 130.04 million hectares of land under cultivation. What is the average amount of cultivated land in sq
km that supports each person (100 hectares =1 sq km = 247 acres)?
130 million hectares x
1 sq km = 1.3 million sq km. Per person would be 1.3 million = 1,000 sq km
100 hectares
1284 million
person
3. At the end of 2002, there were 502 million urban residents. What percentage of the total population were living
in cities?
Percentage = Amount of interest x 100 = 502 = 39%
Total Amount
1284
4. At the end of 2002, there were 661.15 million males in China. What percent of the total population were males?
661 x 100 = 51% males
1284
5. 22.4% of China’s total population was in the age group of zero to age fourteen. How many children is that? If the
average number of students in each elementary school is 500, how many elementary schools are needed in
China (assume that all children between the ages of 0 and 14 attend)?
Amount of interest = Percentage (in decimal form) x Total amount
0.224 x 1284 = 288 million children / 500 children per school = 576,000 schools
6. In 2002, 16.47 million babies were born in China. What was the birth rate (as a percentage and per 1000 – also
known as crude birth rate)?
Birth Rate = (# of births per year) x 100 = 16.47 x 100 = 1.28%
CBR = 12.8/1000
(Total population)
1284
7. In 2002, 8.21 million people died in China. What was the death rate (as a percentage and per 1,000)?
Death Rate = (# of deaths per year) x 100 = 8.21 x 100 = 0.64%
CDR = 6.4/1000
(Total population)
1284
8. What was the total overall growth rate of China’s population in 2002?
r = (births – death)
= (16.47 – 8.21) = 8.26 = 0.64%
(total population)
1284
1284
9. Using the rate from question 8, how many years will it take for China’s population to double?
Rule of 70 =
70
= 70 = 109 years
r (in percent)
0.64
10. In 2002 about 1.1 million cars were sold in China. In 2003 a little more than 2 million cars were sold. What was
the percent increase in car sales?
Percent change =
change (which is the difference between new and old) x 100
Original amount
= 2 – 1.1 x 100 = 0.9 x 100 = 82%
1.1
1.1
11. Most people living in urban China use bicycles for transportation. Only three people per 1000 actually own a car.
How many people own cars in China?
1284 x 3 car owners = 3.85 million people
1000 people
12. Oddly, while China has relatively few cars on the highways compared to the size of its population, they have the
highest number of traffic fatalities in the world: more than 100,000 per year. What is the per capita death rate in
China for car fatalities?
Per capita means per person.
100,000 = 0.0000779 accidents per person
1284 million