There is a virus turning people into zombies who attack the living and never die. No one knows where it came from, but when the virus was first detected, it was 3 days after a group of 20 archaeologists had opened up an ancient tomb. Unfortunately, all 20 archaeologists had been turned to zombies. Authorities believe the virus is spread when infected people bite someone who's uninfected. Each zombie bites 2 uninfected people each day. How many zombies were there at day zero (i.e. t =0)? If the number of zombies Z(t) takes the form Z(t) = Aekt, where A is the number of zombies at t = 0, what is k, the estimated growth rate of the virus? How long will it take before the entire human population of the planet (which for this problem will be taken as 7 billion people) are turned into the undead?