Double-check your napkin

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 R0 = 2, then each infected person infects two more.  So R0 is the base of the exponential function y = R0^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, …

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?