The real exponential growth existential threat to the world is not grey goo nano robots but Rambo.
The number of people killed per minute doubles in every Rambo film
Number of people killed per minute in the Rambo series.
* Rambo: First Blood (1982): 0.01
* Rambo: First Blood Part II (1985): 0.72
* Rambo III (1988): 1.30
* Rambo IV (2008): 2.59
So say the film is 90 minutes long. There are 6000 million people in the world. So Rambo needs to kill 66 million people per minute to kill everyone.
Currently in Rambo 4 he is killing 2.59. So at the current growth rates of blood lust in Rambo 30 everyone on earth will be killed.