I created this mini project to launch our exponential functions unit in Algebra 1 this year, which came right after a mini unit reviewing linear functions. Instead of telling students the power of exponential growth, I decided to let them figure it out by doing this assignment. Students begin with a Warm Up that asks them to choose between two extra credit offers - one exponential with a low start value and one linear with a higher start value. This sets up a class discussion about predicting which function would grow faster and why. Then, students resolve the debate by completing the first part of the lesson - an exploration into the two extra credit options over 14 days. They find that the exponential growth outpaces the linear within a week, even though linear had a head start.
Then, they do another exploration into the spread of a zombie virus. The 2 different viruses both start with 1 sick person (patient zero) and differ only in the rules of infection, which results in different rates of infection. After filling out tables showing numbers of zombies over the first 30 days of each virus, students then graph the first 14 days of both viruses on the same grid. This allows them to see the clear difference between linear and exponential growth.
Lastly, students extend their knowledge to estimate how long it would take particular numbers of people to be infected by each virus. For linear, this can be done using the formula or by guessing and checking. At the Algebra 1 level, the exponential must be done by guessing and checking. It is pretty powerful for kids to see how quickly the entire world would be infected by the exponential zombie virus. They then finish out with 3 summarizing closing questions to reflect on the entire assignment.
My kids LOVED this day. They were super engaged and had rich conversations about what they were seeing the numbers do. A totally unplanned but really cool effect on this lesson was that my students asked me tons of questions about virology and epidemiology. Be prepared in case your kids do the same! They were really curious about the biology of disease as they worked through this assignment, which is why I am also listing this as a science resource.
Because the common core HS standards emphasize so much the comparison of different types of functions, this type of lesson is perfect for today's Algebra 1 classroom.
I hope you love it as much as I did!