**Understanding this curve can help avoid catastrophe.**

Today’s world is defined by change. Advances in technology, consumer empowerment, and instant gratification are just some of the moving parts of life that are pushing us to a new reality. Change, at the speed of life, is the rallying cry of business and many aspects of society. And along the way, we also can hear the other cry of innovation: fail fast.

This idea of transformational speed in today’s technological word is often captured by a concept extracted from our forgotten books on math and science. The first and most common is linear growth. From marketing to our personal IRAs, this simple line is both easy to understand and to project into the future. A fixed percentage allows us to plan and establishes a clear benchmark for growth and success. For many, it’s math 101 and the basis for simple as well as complicated analytics.

But as we know, the world isn’t flat. It’s becoming an exponential world where change is a far cry from that linear dynamic. And that’s when we see the second concept from our old school textbook — exponential growth. In mathematics, exponential growth is something that grows at a rate proportional to its size. More simply stated, the larger a number gets, the faster it grows.

Let’s do a simple example. If I gave you a penny and promised to double the quantity every day, by day 30, you would have $5,368,709. It’s really an amazing transition — over a million dollars in a single month! The biggest changes in the amount occur in the last few days. If we decreased the timeline by just 10% or 3 days to 27 days, the new total would be dramatically less: only $671,088.

This is exponential change, and it comes in a variety of sizes and shapes. We often see it as traditional market dynamics like the adoption of the smartphone or a politically resonant social media post. In other words, it’s when something goes viral!

But the exponential path can be tricky. The rapid upward slope of change typically starts with a slow, smooth, and almost flat trajectory. When this curve is aligned with traditional linear growth, it can appear that the linear model is doing better than the exponential model (see the figure above). In retrospect, we can see how the exponential…