"One bacterium is put in a bottle at 11:00 a.m. and it is observed that the bottle is full of bacteria at 12:00 noon. Here is a simple example of exponential growth in a finite environment. This is mathematically identical to the case of the exponentially growing consumption of our finite resources of fossil fuels.
That shows such a poor understanding of exponential growth that it makes me think this person should not be teaching physics.
First of all, exponential growth basically doesn't ever actually occur in nature: everything has a carrying capacity. Sometimes the carrying capacity is so high it doesn't matter, but clearly in the case of the bottle it does. The growth will slow down significantly as the bacteria approaches the capacity of the bottle. The bottle could easily be half full as early as 11:30 as the available food for the bacteria starts becoming scarce enough to limit its growth.
Secondly, 2^60 bacteria would weigh about 1,100 kg. Assuming the bottle is 1L (larger than a standard wine bottle), you'd need over 1000 bottles to house that much bacteria. So no, if it doubles every minute, then the bottle has been full for the last 10 minutes.
I'm being generous and assuming some process is keeping the flask continuously well-mixed, otherwise you don't even have exponential growth in the ideal case (it's limited by the expanding surface area of the colony).
You might think I'm being pedantic, but the entire exercise is to put some "real world" context to blow the minds of people and illustrate how exponential growth "really" works. But that's not how exponential growth really works in the real world, at all. Instead it's just taking a model of spherical cows to an absurd conclusion that only serves to further confuse people's understanding of the world. It's like those awful anti-intuition-pumps (intuition sinks?) about stretching all your DNA from end-to-end.
This does not answer my question, unless you also have proof that the amount of cases of the ISS crew having to take shelter is also increasing exponentially. Since the astronauts went back to work after 1 hour instead of moving back to Earth, we can infer that the perceived danger has passed.
(That is quite beside the point that Kessler syndrome at that altitude is definitely not the type of "exponential growth in a finite environment" that the linked article describes, because orbital decay means that the smaller the particles get, the faster they will deorbit themselves)
