Citizen Math used to be called Mathalicious. If you have a current account on Mathalicious, you can use those credentials to log in to your Citizen Math account. Learn more here.  # Billions & Billions

## How is the human population changing? 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

• The global population is growing exponentially
• As the population grows, two other things grow with it: the Gross World Product and the amount of CO2 in the atmosphere.
• The developing world is currently growing more quickly and contributing more to CO2 than is the developed world…but the developed world is disproportionally responsible for getting CO2 levels to where they are now.

### MATH OBJECTIVES

• Given two data points, calculate growth rate as a percent
• Build and evaluate an exponential function in a real-world context
• Analyze graphs showing roughly exponential relationships

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 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.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. (a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (c) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 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.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.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.8 Look for and express regularity in repeated reasoning.