If you haven’t, this TechCrunch article is a useful summary: essentially, exponential organisations combine an abundant resource (for example, spare capacity in private cars) with technology to create a business whose growth does not follow the normal incremental model. And the pace of technological innovation means that taking advantage of breakthroughs such as robotics or 3D printing to create these businesses is becoming easier and easier.
The HBR article discusses the fact that creating an exponential business model also requires a different mindset to the normal incremental approach. It’s worth reading it to get the full detail, but some of the key points are that an exponential mindset involves embracing uncertainty, empowering others rather than controlling and directing, and holding your nerve through the stages before growth takes off. In this way the article presents it as the opposite of the classic business approach which relies on a clear plan with fixed milestones, a directed strategy and a solid linear growth pattern.
Some might argue that the classic business plan has always to some degree been a work of fiction, and that any startup must always embrace uncertainty and change in order to succeed, but the article certainly provides interesting food for thought.