## What Is a Growth Curve?

A growth curve is a graphical representation of how a particular quantity increases over time. Growth curves are used in statistics to determine the type of growth pattern of the quantity—be it linear, exponential, or cubic. Once the type of growth is determined, a business can create a mathematical model to predict future sales. An example of a growth curve is a country's population over time.

### Key Takeaways

- A growth curve is a way to visually represent the growth of some phenomena over time, either in the past or into the future or both.
- Growth curves are typically displayed on a set of axes where the x-axis is time and the y-axis quantifies the phenomenon in question.
- Growth curves are readily used in a variety of applications from population biology and ecology to finance and economics.

## Understanding Growth Curves

The shape of the growth curve can make a big difference when businesses determine whether to launch a new product or enter a new market. Slow growth markets are less likely to be appealing because there is less room for profit, while exponential growth could mean that the market could see a lot of competitors enter the market.

Growth curves began in the physical sciences such as biology; today, they're a common component to social sciences as well. Advancements in digital technologies and business models now require analysts to account for growth patterns unique to the modern economy. For example, the winner-take-all phenomenon is a fairly recent development brought on by the likes of Amazon, Google, and Apple. Researchers are scrambling to make sense of growth curves unique to their business models and platforms.

Future shifts in demographics (aging), the nature of work, and artificial intelligence will further strain conventional ways of analyzing growth curves or trends.

The expression growth curve might be considered more reserved for scientific approaches to what the layman may describe as growth trends. Definition aside, growth curves play an essential role in determining the future success of products, markets, and societies, both at the micro and macro levels.

## Example: Exponential Growth of Populations

In the image below, the growth curve displayed represents the growth of some population (in millions) over a span of decades. This shape of a growth curve is considered to be exponential growth, where the growth curve starts slowly, remaining nearly flat for a time before increasing swiftly as to appear almost vertical. It follows the general formula: V = S * (1 + R)^{t }

The current value, V, of an initial starting point subject to exponential growth, can be determined by multiplying the starting value, S, by the sum of one plus the rate of interest, R, raised to the power of t, or the number of periods that have elapsed.

In finance, exponential growth appears most commonly in the context of compound interest. The power of compounding is one of the most powerful forces in finance. This concept allows investors to create large sums with little initial capital. Savings accounts that carry a compounding interest rate are common examples.