Introduction to Population Math

Homework 1/8/2018 Take notes on the equations and example problems (Slides 1 – 21) in your notebook. You will complete the practice problems at the end (Slides 23+) in class on Wednesday.

Important Equations (#’ed) & Practice Problems 1. Growth Rate (r) r = (births + immigration) – (deaths + emigration) Total Population r as a percent (multiply by 100%)

If a city with a population of 30,000 experiences 100 births, 40 deaths, 10 immigrants, and 30 emigrants in the course of a year, what is its net annual percentage growth?

If a city with a population of 30,000 experiences 100 births, 40 deaths, 10 immigrants, and 30 emigrants in the course of a year, what is its net annual percentage growth? (b + i) – (d + e) = (100 + 10) – (40 + 30) Total population 30,000 people = 40 = 0.0013 x 100 = 0.13% 30,000

CBR/CDR (Crude birth rate/ crude death rate) 2. Birth/Death Rate # births/deaths per year (x 100 for %) Total Population CBR/CDR (Crude birth rate/ crude death rate) # births/death per 1000 people

The United States experiences 4 million births per year The United States experiences 4 million births per year. What is the birth rate for the US? **Memorize: US population is 320 million.

The United States experiences 4 million births per year The United States experiences 4 million births per year. What is the birth rate for the US? **Memorize: US population is 320 million. 4,000,000 or 4 million 320,000,000 320 million = 0.0125 or 1.25%

For every 100 people in the United States, 2 die For every 100 people in the United States, 2 die. What is the CDR for the US?

For every 100 people in the United States, 2 die For every 100 people in the United States, 2 die. What is the CDR for the US? CDR = # deaths 1000 people 2 deaths x 10 = 20 deaths/1000 people 100 people 10

4. Doubling Time (how long it would take a population to double in size) Rule of 70 70 = Doubling time (in years) r (in percent)

If a population grows at a rate of approximately 5 percent per year, how many years are required for the population to double?

If a population grows at a rate of approximately 5 percent per year, how many years are required for the population to double? Rule of 70! 70 = 14 years 5%

Population Density (amount of people per amount of area) Population Density = Population Area

There are 2. 7 million people in Chicago There are 2.7 million people in Chicago. What is the population density of Chicago, assuming its area is 606 km2?

There are 2. 7 million people in Chicago There are 2.7 million people in Chicago. What is the population density of Chicago, assuming its area is 606 km2? 2,700,000 people = 27,000 = 4500 people/km2 600 km2 6

Per Capita = Per Person Amount of interest Number of people

The United States’ net worth is 86. 8 trillion ( x 1012) The United States’ net worth is 86.8 trillion ( x 1012). What is the per capita net worth of the US?

The United States’ net worth is 86. 8 trillion ( x 1012) The United States’ net worth is 86.8 trillion ( x 1012). What is the per capita net worth of the US? 86.8 x 1012 = 86.8 x 106 = $270,000 /person 320 x 106 320

Percent Increase Final amount – Initial x 100 = % inc. Initial

The city of Brentwood welcomed 3,000 new residents this fall The city of Brentwood welcomed 3,000 new residents this fall. What was the percent increase in the population of Brentwood? (original population is 55,000 people).

The city of Brentwood welcomed 3,000 new residents this fall The city of Brentwood welcomed 3,000 new residents this fall. What was the percent increase in the population of Brentwood? (original population is 55,000 people). 58,000 – 55,000 x 100 = 3,000 x 100 = 5.5% increase 55,000 55,000

Practice Problems If a population of 100,000 experiences 2,000 births, 1,600 deaths, 200 immigrants, and 100 emigrants in the course of one year, what is its net annual percentage growth rate? If the % annual growth rate is 8%, what is the doubling time in years? If the doubling time is 7 years, what is the % annual growth rate? A bank advertises doubling your investment money is 12.3 years. What percent simple interest will it be paying?

5. The world population grows at a rate of 1.2% annually. What is the doubling time for the world population? What would be the doubling time if the growth rate is cut to 1%? Assuming the growth rate stays constant (at 1.2%), how many doublings would take place in a 500-year period? What would the world’s population be in 500 years if there are currently 7 billion people? (Think: one doubling is how long? So after that time you’d have 14 billion. Then you’d have 28 billion after a second doubling time had passed… etc.)

One thousand two hundred and seventy deer are living on a island that is eight hundred and thirty square kilometers in size. What is the population density of the deer per square kilometer? A city with 53,340 people has 876 births. What is the birth rate? (as a percent and CBR-per1000) In 1990, there were 1.2 billion people living in China. At the end of 2002, there were 1280 million people. What was the percent increase in China from 1990 to 2002? What was the annual percent increase?

Answers – You’re Welcome 0.5% 6. 1.5 deer/km2 8.75 years 7. 1.6% / CBR: 16/1000 10% 8. 6.7% 5.7% a. 58 years b. 70 years c. 8 doublings d. 1.8 trillion