Exponential growth is growth that feeds on itself — growth generated by a reinforcing-feedback-loops in which the size of a stock multiplies the rate at which the stock grows. The result is a constant percentage rate of increase, which means an ever-growing absolute rate of increase, which means a characteristic doubling time: a stock growing at 2% per year doubles every 35 years; at 7% per year, every 10 years; at 70% per year, every year (using the rule of 70: divide 70 by the percentage growth rate to get the approximate doubling time).
The doubling-time insight was central to limits-to-growth-1972. jay-forrester, dennis-meadows, Meadows, jorgen-randers, and william-behrens-iii used it to show that the quantities most people took as manageable growth rates — a few percent per year — implied dramatic futures over decades. World population growing at roughly 2% per year in the early 1970s would double in 35 years; industrial output growing faster would double sooner. In a finite world with finite resources, the carrying capacity sets a hard limit that exponential growth would eventually encounter.
Meadows returned repeatedly to the intuitive failure that makes exponential growth so dangerous: human intuition is calibrated for linear change. When a quantity doubles (from 1 to 2, from 2 to 4, from 4 to 8), each doubling seems like the same amount of additional growth as the previous one. In absolute terms, the sequence is 1, 2, 4, 8, 16, 32 — each step adds as much as all previous steps combined. A lake in which algae covers 1% of the surface, doubling each week, will appear manageable for weeks; when it covers 50%, it will cover 100% in one more week. The problem is not visible until it is nearly too late.
The policy implication Meadows drew was that exponential growth in a finite system must eventually encounter a balancing limit — the question is only whether that encounter is smooth or abrupt. If delays-in-systems are short and the resource base is not degraded by the overshoot, the growth can level off in an S-curve. If delays are long and the resource base is degraded, overshoot-and-collapse results.
Exponential growth is not inherently bad in Meadows's framework: the growth of knowledge, of renewable energy capacity, of institutional capacity for cooperation could all be exponential and beneficial. The issue is the interaction between exponential growth in physical throughput (resource use, waste production) and the finite physical carrying capacity of the planet. This is why the limits-to-growth-1972 analysis focused specifically on material and energy flows rather than on all forms of growth.
mit-system-dynamics-group's world model (which became the Limits to Growth model) used exponential growth as its starting assumption for all major variables, then asked: what happens when these trajectories interact within a finite system? The scenarios showed that the precise parameter values mattered less than the exponential structure: the model was "robust to doubt" in the sense that very different parameter choices still produced overshoot in most scenarios, because the underlying dynamics of exponential growth in a finite world are not parameter-sensitive.