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Billions & Billions (Updated!)

What are the consequences of human population growth?

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Billions & Billions (Updated!)

What are the consequences of human population growth?

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Billions and Billions - Student Handout.pdf
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Billions and Billions - Teacher Guide.pdf
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2023-2024 Versions

In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

Scientists estimate that on Halloween 2011 the global population reached 7 billion. But how long did it take humanity to grow to this level, and how large should we expect our population to become?

In this lesson, students will explore how many people the Earth is adding and losing each minute, and use this to build an exponential model for human population growth. They’ll also predict what the world population will be in the future and discuss the environmental consequences of population growth and economic development.

REAL WORLD TAKEAWAYS

  • Since 1900, the global human population has grown exponentially.
  • As the human population has grown, so has the amount of carbon dioxide in the atmosphere and the sea level.
  • Today, the human population is growing fastest in so-called “developing” countries that are less wealthy and currently industralizing, while the population is growing less quickly in “developed” countries that are wealthier and have already industrialized. Because less wealthy countries often depend on inexpensive and more pollution-producing sources of energy (e.g. coal), their industrialization risks exacerbating climate change. Allowing them to industrializing cleanly may require support from other countries.

MATH OBJECTIVES

  • Given two data points, calculate the change in both absolute terms (e.g. additional people per year) and as a percent.
  • Discuss the appropriateness of a linear vs. exponential model for a given situation.
  • Create an exponential function to forecast into the future.
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.
Algebra 1
Exponential Functions (Beg.)
Algebra 1
Exponential Functions (Beg.)
Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. F.BF.1 Write a function that describes a relationship between two quantities. (a) Determine an explicit expression, a recursive process, or steps for calculation from a context. (b) Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (c) (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Mathematical Practices MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.8 Look for and express regularity in repeated reasoning.

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