Comparing Linear and Exponential Growth (HSF.LE.A.1)One of my favorite lessons that I teach is an introduction to exponential functions. In this lesson, students compare the population growth of different states, some of which exhibit linear growth, and some of which exhibit exponential growth. There are lots of ways you could introduce this. First, you could ask students which states they think would grow exponentially. If they have had practice with exponential growth then they may understand that exponential growth is quicker than linear. Which states probably have faster growth? Why?
Then I show students a select group of six graphs representing six states' population growth. Three of them are clearly linear and three of them are exponential. This can be a great way to introduce the shape of an exponential function! Students can easily differentiate between the familiar shape of a linear function and the new shape of the exponential curve. The corresponding worksheet guides students through sorting the states by the shape of their graphs, and then interpreting the features of the graph in terms of the problem situation. Additionally, students are asked to brainstorm what factors affect population growth and why we collect population data. Lastly, students analyze the graphs of states whose population decreases over certain decades, such as Kansas and Oklahoma from 1930-1940.
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