How to Survive a Zombie Attack

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems using models of exponential functions.

On June 30, 2035, a sleeper cell of zombies executed an evil plan 10 years in the making.  Their objective: "turn" the

entire human race into evil zombies!  Each zombie can turn 3 humans per day, but they are not sure how long it will take them to completely turn every human on the planet.  Complete the table below to show how many zombies there will be every day for the first 10 days of the attack.  The original sleeper cell had only 5 members.

1. As the days go by, what patterns of growth do you notice in the number of zombies turned each day?

2. What would this data look like on a graph? Use Desmos to graph the data for days 0-10.

3.  From the table or graph:

1. How many zombies are turned on day 10?
   

1. What would you have to multiply this number by to get the number of zombies created on day 11?
   

1. How would the entire table table change if instead of starting with 5 zombies, we started with only one zombie? 
   
   
   
2. How long would it now take for the zombies to take over the world? Assume the population of the world is 6,975,000,000 and we started with 5 zombies. Explain how you got your answer.

4. Which one of the equations below would correctly model the number of zombies turned each day if you start with 5 zombies? Explain.

	y = 5x3			y = 3(5)2

5. What does the variable, x, represent in the equation you chose from #4?

6. Write an equation to model the number of zombies turned each day if you start with 12 zombies and each can turn 6 people per day. How long would it now take the zombies to take over the world?

7. If you were given the choice between starting with more zombies at a slower growth rate or starting with fewer zombies at a greater growth rate, which would you choose and why?

Within 3 days of the initial attacks being reported, a group of scientists quickly began working to find an antidote for "zombieism".  Within a few short weeks, they had one. Unfortunately, their antidote was found to be successful only 15% of the time.  Make a table showing how many zombies were cured after 10 rounds of administering the antidote (assume every remaining zombie is given the antidote in every round and no new zombies are created).

 8. What patterns of "decay" do you notice in the cumulative number of zombies remaining after each round of the antidote's administration? (hint:  If 15% of the zombies are cured, then how many remain?)

9. What would this data look like on a graph? 

Use Desmos to graph the first 10 rounds of administration of the antidote.

10. Write an equation to model the pattern in the data.

11. At this rate, how long will it take the scientists to completely turn all zombies back into humans?  Can this ever really happen?  Why or why not?

12. Write your answers (the equations) to #4 and #10 below. What similarities and differences do you notice in the equations developed for both the initial attack and the antidote phases? 

13. Use your equations from #12 above to answer the following:

1. Which value in each equation impacts whether or not the initial value will increase or decrease over time?  Give a short explanation.

1. Which value in each equation tells us what the initial value is? Give a short explanation.

Research Link-Canadian mathematicians and authors of “When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infections” published in the  journal of “Infectious Disease Modelling Research”, concluded that the secret to our survival is to hit zombies with everything we have... hard, fast and early.  Using what you have learned about exponential growth in this worksheet, why do you think these scientists came to that conclusion?

Adapted by Frederick County AFDA teachers