The graphs below illustrate the 4 possible behaviours of exponential growth. The growth could be either population or industrial production:
1. Continuous growth: If physical limits are very far off or are themselves growing.
2. Sigmoid growth: If signals from physical limits are instant and responded to immediately or the population limits itself without needing signals.
3. Overshoot and oscillation: Results if signals or responses are delayed and limits are unerodable or are able to recover quickly from erosion.
4. Overshoot and collapse: Results if signals or responses are delayed and limits are erodable (irreversibly degraded when exceeded).
In the case of the Earth, there is a delay between the signal of overshoot and the response, and limits are erodable. So overshoot and collapse is the mode of behaviour that is likely to result.