The 2011 movie *Contagion *required viewers to appreciate the speed at which infection can spread. The term “R-nought” is used to represent the reproductive rate: If ** R_{0}** = 2, then each infected person infects two more. So

**is the base of the exponential function y =**

*R*_{0}**^x, where x is the number of time steps. However, Jude here seems to have a different take on the function, spitting out the terms 2, 4, 16, 256, …**

*R*_{0}You might think about asking your students

- In the sequence 2, 4, 16, 256,…

What are the next several terms? Is the 30th term close to a billion? What is the recursive formula for the sequence? - If you start with 2 infected people, and each infected person will infect 2 others, give the number of new infections for the first few time steps. What about
*total*infections for the first few time steps? Can you figure out how many people will have been infected after 30 time steps?

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