Yet another systems thinking classic is the riddle of the French farmer and the lily pads. This requires reasoning about exponential growth.
This may be too easy without the typical complex setup of the riddle, but I’d say the AI nailed it again.
Don't just do something, stand there! Reflections on the counterintuitive behavior of complex systems, seen through the eyes of System Dynamics, Systems Thinking and simulation.
Android activations are apparently growing 4.4% per week, on a basis of around 100 million sales per year.
By the rule of 72 for exponential growth, that means sales are doubling every 16 weeks, or about three times per year.
If sales are growing exponentially, the installed base is also growing exponentially (because the integral of e^x is e^x). Half of the accumulated sales occur in the most recent doubling (because the series sum 1+2+4+8+…+n = 2*n-1), so the integrated unit sales are roughly one doubling (16 weeks) ahead of the interval sales.
Extrapolating, there’s an Android for everyone on the planet in two years (6 doublings, or a factor of 64 increase).
Extrapolating a little further, sales equal the mass of the planet by about 2030 (ln(10^25/10^8)/ln(2)/3 = 19 years).
Limits? What limits?