# How to Survive a Zombie Attack (understanding exponential growth and decay).

Authors:  Erin Ondrusek, Kelli Jurek and Arthur Weiss

Zombies... I love 'em... who doesn't????

Our A4A group put together an investigation that used a zombie outbreak as a model for exponential growth and a cure for zombieism to model exponential decay.

Click the link below to access the investigation at Google docs:
Google docs allows you download the application and print... regardless your computer or operating system (PC, Mac, linix, etc...)  As long as you can access the web, you can get this investigation at the link above.

The idea of using a zombies apocalypse to model exponential growth came to our group at around Halloween.  At about that same time a group of Canadian mathematicians researching infectious disease wrote a paper for Nova Science Publishers using "zombieism".  Although not a real world situation the exercise does provide many opprotunities for mathematical modeling and problems solving. If you are interested in this article check it is free to download (for now) at www.mathstat.uottawa.ca/~rsmith/Zombies.pdf

The exercise is designed to be light hearted, fun and instructional.  If you need additional preparation, you may want to review one or more of the following before teaching the lesson:
Or just do what I do... watch "Thriller" over and over and over and over and over again.

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### Replies to This Discussion

this looks like a great time!
Thank you for sharing this!!

It woked great in my Advanced Algebra class prior to starting a unit on exponential equations. I referred back to this activity and the student's results as I taught the unit. The students seem to gain a greater understanding of exponential growth based on their work done and it was the talk of the high school for a couple of days!
I'm glad to hear it was a success. Thank you for your comments.

I have a number of other worksheet/investigations that can be downloaded by clicking this link.

I have a web page, but recently took it off line to work on to further... so, if you like, you can have direct access to my google folder by clicking the link above. If you liked the zombie investigation, you may also like the investigations on correlation:
U2E1-E3... Correlation investigations and "correlation does not mean causation"

Thanks again
If you're interested in a whole course on Zombies:

I've already sent Dr. Blumberg a message at his blog with a link to the A4A lesson "how to survive a zombie attack" we made last year and another math/zombie paper just in case he wanted to incorperate a little math into his new class...
Thanks for sharing this activity. I will be using this in the spring when I begin my exponential functions unit. I think it will be a great hook for the unit and there is tremendous possibility for follow up discussions. Thanks again for posting.

I think this project is great. However, I've just assigned it to one of my classes and the issue some of the students brought up, which I agree with, is that when each zombie creates 3 new zombies, that's a total of 4 zombies for every original zombie, not 3.

If each zombie were creating only 2 zombies in addition to itself, everything would work perfectly.
day 0: Zombie 0A, Zombie 0B, Zombie 0C, Zombie 0D, Zombie 0E.
Each Zombie makes only 2 new zombies by day 1.
day 1:
0A -> 1A(1), 1A(2)
0B -> 1B(1), 1B(2)
0C -> 1C(2), 1C(2)
0D -> 1D(1), 1D(2)
0E -> 1E(1), 1E(2)
=15 zombies
(the day 1 zombies are still there)
All 5 of the "day 0" zombies and all 10 of the "day 1" zombies each make 2 new zombies by day 2
day 2
0A     -> 2A(1), 2A(2)
1A(1) -> 2A(3), 2A(4)
1A(2) -> 2A(5), 2A(6)
0B     -> 2B(1), 2B(2)
1B(1) -> 2B(3), 2B(4)
1B(2) -> 2B(5), 2B(6)
0C     -> 2C(1), 2C(2)
1C(1) -> 2C(3), 2C(4)
1C(2) -> 2C(5), 2C(6)
0D     -> 2D(1), 2D(2)
1D(1) -> 2D(3), 2D(4)
1D(2) -> 2D(5), 2D(6)
0E     -> 2E(1), 2E(2)
1E(1) -> 2E(3), 2E(4)
1E(2) -> 2E(5), 2E(6)
= 5 "day 0" zombies, 10 "day 1" zombies, and now 30 "day 2" zombies
=45 zombies
So there you go. Each zombie only makes 2 extra zombies, and the rate of growth is 3^x.

The question my students are having is that if you start with 5 zombies and they each turn 3, there are now 15 NEW zombies, but 20 zombies altogether and if each of those turn 3.....This isn't modeling 5*3^x any more...