DO The Math PREPARING TO DO THE MATH Four math topics that have shown up on multiple-choice released exams are 1. Calculating global growth rate (including CBR, CDR & etc) 2. National population growth rate 3. Doubling time 4. % growth Both calculations are similar but students often get them confused. 1. Global Growth Rate: The formula for calculating this demographic statistic Global population growth rate = [(CBR) (CDR)] 10 It explains that the crude birth rate (CBR) is the number of births per 1,000 individuals per year. The crude death rate (CDR) is the number of deaths per 1,000 individuals per year (see explanation below**). The rate is expressed mathematically as EXAMPLE: Global population growth rate = [(CBR) (CDR)] = [(20) (8)] = 1.2% 10 10 2. Nation s Growth Rate: The formula for calculating a nation s growth rate is a little different. While nations experience immigration and emigration, the global population does not. We are all one global population. National population growth rate = [(CBR + immigration)] (CDR + emigration)] 10 EXAMPLE: Country X growth rate in 2007 = (16 + 6) - (8 + 0) = 22 8 = 14 = 1.4% growth rate of country X 10 10 10 **What is CBR,CDR, I and E? How to find crude anything rates (i.e. CBR, CDR, I & E): Use the numbers for births, deaths, immigrants or emigrants and divide by the total population as stated in the problem. Then set up a proportion equal to x divided by 1 thousand and solve. This results in a number that can easily be used to compare different cities, countries using the same denomination. (i.e. you can compare like entities). NOTE: The text books DO NOT tell you that I and E or immigration and emigration rates are derived exactly the same as crude birth and death rates. Just use the following formula and substitute different numbers (# deaths, immigrants or emigrants) depending on which rate you need. # Births = X Total population 1,000
3. Doubling time: This is the time it takes to double the population using the calculated growth rate. Use the growth rate ( r) in the following formula: DT = 70 = years r 4. Percent growth: Calculate this by dividing population change by the total population, multiply by 100 to get the rate. New population Old population X 100 = % Total population Note: a. this last formula is a different way of arriving at the same figure as the global and national growth rates! b.
Population Worksheet Name: Per from Dan Hyke & C. Schneider, Oct 2004 adapted 8/09, 2014 Hedges FOR THE QUIZ: SHOW YOUR WORK!!! To earn full credit for your answers, you must show the appropriate formula (1 pt), the correct substitutions (1 pt), and circle your answer including the correct units (2 pt) (4 points total) COPY ALL FORMULAS HERE General Population Growth: National population growth Doubling Time NEW %Growth GENERAL 1. A city with 53,340 people has 876 births. What is the birth rate (as a percentage and per thousand)? 2. Another city experiences 12 deaths for each thousand people. What is the death rate (as a percentage and per thousand)? 3. A village of 23,473 people has 2,342 births and 473 deaths. What is the growth rate for this village? 4. A small country of 744,785 people has 44,678 immigrants and 12,567 emigrants. They also experience 15,898 deaths and 35,665 births. What is the growth rate of this small country?
5. How many years will it take for this country to double its population? 6. If a country were doubling its population every 35 years, what would its growth rate be? CHINA At the end of 2002, there were 1,284.53 million people living in China... 7. * A) China is the third largest country in the world with an area of 9.6 million square kilometers. B) What is the population density of China? 8. *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) 9. At the end of 2002, there were 502 million urban residents. What percent of the total population were living in cities? 10. At the end of 2002, there were 661.15 million males in China. What percentage of the total population were males? 11. 22.4% of China s total population was in the age group of zero to age 14. 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 every child, age zero to 14 attends) 12. In 2002, 16.47 million babies were born in China. What was the birth rate (as a percentage and per 1000)? 13. In 2002, 8.21 million people died in China. What was the death rate (as a percentage and per 1000)?
14. What was the total overall growth rate of China s population in 2002? 15. Using the rate from the previous question, how many years will it take for China s population to double? CANADA 20. *In 2000, there were 30,750,087 people living in Canada, which has a total area of 9,984,670 km 2. What was the population density of Canada? 21. *In reality, there are a lot of fresh water lakes in Canada, about 891,163 km 2 of lakes. What was the population density of terrestrial Canada in 2000? 22. In 1999 with a beginning population of 30,491,000 people, there were 335,500 births in Canada. What was the birth rate, expressed as per 1000? 23. In Canada during the same year there were 225,500 deaths, 205,711 immigrants and 41,142 emigrants. What was the growth rate for Canada, expressed as a percentage? 24. How many years will it take for Canada s population to double? Doubling Time Problems 1. The world population in 1992 is 5.42 billion. If its population doubled every a. 41 years, what would its population be in 41 years? b. 41 years, what would its population be in 82 years? c. 82 years, what would its population be in 164 years?
2. A country has a doubling time for its people of 20 years. If it ends up with 80 million people after 60 years, how many people did it have to start with (in this question)? 3. Human newborns usually weigh about 7.5 lb. at birth. They double that in 6 months. If its weight continued to double every six months, how much would an average 5 year old weigh? 4. E. coli, a type of bacteria, divides once every 15 minutes. Calculate how many will exist after 24 hours if their biotic potential is infinite and its environmental resistance is zero.
ANSWERS (* denotes challenge questions that use DA, i.e. dimensional analysis) Problem # Numeric Units answer 1 16.4 CBR or no units 2 0.12 % 3 7.96 % 4 6.7 % 5 10.45 years 6 2 % 7* 133.72 Chinese per km 2 China 0.001 km 2 8* 9 39.1 % 10 51.49 % 11 575232 schools 12 12.83 CBR 13 6.32 CDR 14 6.43 % 15 108.8 years Canada 20* 3.08 Canadians Per km 2 21* 3.382 Canadians Per km 2 terrestrial 22 11 CBR 23 0.9 % 24 77.74 years DT 1a 10.84 Billion people 1b 21.68 Billion people 1c 43.36 Billion people 2 3.5 % 3 30,720 lb 4 7.9^28 bacteria
FRQs 2000/4 Pop. Pyramids X, Y, Z Which countries have the largest rate of population growth? Which has the smallest? Compare infant mortality rates for countries X and Y. What are the changes in both birth rate and death rate for a country making the transition from a preindustrial to an industrial society? Describe an incentive that the government of a country could offer its citizens that would favor a reduction in the growth rate? 2003/2 Fictional country that is tracking its population data Create a graph, plot both the crude birth rate and crude death rate Calculate the annual growth rate in 1950. Calculate the birth rate of Industria in 1977. What are two factors that might have accounted for the rapid decline in death rate in Industria? Why might birth rates be higher in 1855 compared to those in 1950? Calculate the population size if annual growth rates remained constant as recorded in 1895. Graphing data on worldwide total fertility Discuss two of the causes for the trend in the worldwide TFR. Identify and discuss two economic or societal factors that account for the difference between TFR of Kenya vs. USA. What are two human activities connected to rapid population growth that are having an impact on the world s biodiversity?