# What Exponential Growth Really Looks Like (And How to Hit It)

Figure out what exponential growth is, what it looks like, how to calculate it, and the strategies that will help you catalyze growth.

Best Practices
November 24, 2023
Julia Dillon
Senior Product Marketing Manager, Amplitude

Exponential growth creates a compounding effect that increases the amount added to a “system” proportional to the amount already present. Exponential growth is desirable to companies, especially startups, when it comes to user and revenue growth.

Want a real-life example of exponential growth? Consider Facebook.

Starting with nearly 1 million users in 2004, it reached over a billion users by 2015. And that growth continued, generating revenue to fuel Facebook’s expansion, acquisition of other social platforms, and the ultimate consolidation of apps and technologies under one brand, Meta. In the first quarter of 2023, Meta reported 3.81 billion people using at least one of the company's core products.

So, what makes Facebook and other companies who have experienced exponential growth successful? Let’s uncover the mechanics behind exponential growth and the steps to harness it for the good of your company.

Key takeaways
• The basic concept behind exponential growth is that the amount added to a “system” is proportional to the amount already present. A “system” can be a population, revenue, a user base, etc.
• The formula for exponential growth is x1 = x0(1+r)t.
• Exponential growth starts with a product-market fit but can then be accelerated by incentivizing referrals, encouraging social sharing, leveraging valuable push notifications, and ensuring a scalable business model.
• Exponential growth won’t last forever, so businesses should set reasonable long-term expectations.

## How exponential growth works

The basic concept behind exponential growth is that the amount added to a “system” is proportional to the amount already present. A “system” can be a population, revenue, a user base, etc. The bigger the system, the greater the increase, meaning growth constantly accelerates with each quantity added to the starting value.

As per the formula below, you can model exponential growth as a mathematical exponential function between variable x growing at a rate r to the power of time t. X0 is the starting value, r is the rate of increase, t is the time in equal intervals or interventions (daily, monthly, yearly, etc.), and X1 is the future value.

The equation may look complicated, but it’s just saying that your current growth rate is proportional to your current size, similar to a compound interest calculation.

Let’s say our growth rate (r) is one, indicating our current value doubles each time we measure it. If in January 2023 we have two paying customers and that doubles each month, the first eight months would look like this:

 Month Jan 2023 Feb 2023 Mar 2023 Apr 2023 May 2023 Jun 2023 Jul 2023 Aug 2023 Customers 2 4 8 16 32 64 128 256

Using this formula, two users after seven months at the growth rate of 100% would be: 2(1 + 1)7 which equals 256 users in August 2023.

256 customers after eight months of hard work doesn’t sound like exponential growth unless it continues over time. Look what happens through 2023 and 2024 if the exponential function continues:

 Month Aug 2023 Sept 2023 Oct 2023 Nov 2023 Dec 2023 Jan 2024 Customers 256 512 1,024 2,048 4,096 8,192 Feb 2024 Mar 2024 Apr 2024 May 2024 Jun 2024 Jul 2024 16,384 32,768 65,536 131,072 262,144 524,288 Aug 2024 Sept 2024 Oct 2024 Nov 2024 Dec 2024 1,048,576 2,097,152 4,194,304 8,388,608 16,777,216

At that same growth rate of 100%, the result after 23 months would be: 2(1 + 1)23, which equals 16.7 million users in December 2024.

And if you continued the formula through June 2025, it would be 2(1+1)29, equalling over 1 billion users.

## How to hit exponential growth

Product managers and entrepreneurs have used many tactics and strategies to hit exponential growth in the real world. The starting point is finding the right product-market fit.

The viral factor of your marketing catalyzes exponential growth. Viral marketing relies on word-of-mouth for users to invite friends, family, and others in their network to use your product. Once they encourage a few of their contacts to buy, network effects kick in to amplify the adoption of your product. Your product becomes more valuable to a larger number of people as more and more people start using it.

So the big question is: how do you catalyze exponential growth?

### Build a great product

Exponential growth is only possible if people love to use your product. They must form a habit of repeatedly using your product to retain them for long-term growth. You don’t want users to abandon your product because it’s too complicated, as that would eliminate the probability of exponential growth.

To understand your product’s ease of use, leverage the “grandma test.” Ask yourself, “Would I refer this product to my grandma?” to help you gauge its simplicity.

You should adopt an obsessive mindset about building something users love and view the product strategy process as a perpetual work in progress.

### Incentivize referrals

Incentivizing product referrals encourages customers to recommend your product, in turn growing your customer base and transforming customers into loyal brand advocates.

Dropbox grew exponentially by 3,900% in just 15 months by incentivizing referrals and building a viral loop into their referral program. They gave an additional 500 MB of space to the referrer and the referee for each successful referral, up to a limit of 16GB.

They also realized that the more people knew about their referral program, the more they would participate. So, apart from offering a meaningful incentive, they also integrated their referral program into their onboarding process to make it more visible.

Dropbox made it easy for users to complete referrals, providing options like sharing a unique referral link or syncing their contacts from their email account. It also gave users more transparency into the referral process with a referral status dashboard.

Every successful referral also triggered a ‘thank you’ email to both the referrer and the referee—with a call to action incentivizing both to invite more friends. Dropbox’s systematic, well-organized approach to its referral program helped it grow from 100k users in September 2008 to 4 million users in September 2017.

### Use social sharing

Sharing information about products on social media acts as an ‘organic product recommendation.’ People typically trust organic recommendations over incentivized ones, which can lead to higher product adoption and an increased chance of exponential growth.

You’ve likely seen your fair share of sweaty post-workout pictures on social media. That’s because many fitness apps encourage users to share their workout metrics via social media to create a sense of achievement and attract praise and engagement with their friends.

Workout posts are a great example of how a product or app can spread the word organically using social sharing. Users are not pressured to share these stats—it’s all done voluntarily by them. The organic nature of social sharing helps attract new users and new growth.

### Provide relevant, valuable information

28% of users uninstall apps because they receive too many ads and notifications. That’s why it’s critical that push notifications and ads are timely, relevant, and valuable to avoid irritating customers.

For instance, Uber notifies its drivers of high-demand areas through push notifications so they can offer rides there to make more money. Providing relevant information helps engage users and increase the likelihood they’ll continue using your product long-term, leading to exponential growth through retention.

### Have a scalable business model

You should adopt a business model or technology stack that allows you to scale efficiently. For example, exponential customer demand for a restaurant could lead to them turning potential customers away. A restaurant can only serve a certain number of customers at any given time, so exponential growth is likely not feasible in this context.

However, exponential growth would be possible for an online travel site that connects hosts with guests for temporary accommodation. Once the platform is built, it could grow by adding new hosts and guests, making it a scalable business model.

## Exponential growth can’t last forever

No business can grow exponentially forever—or even for very long. Startups run out of money, saturate their market, or their techniques stop working. As the visual below demonstrates, the growth rate usually levels off at some point, so you should set reasonable expectations for the exponential growth model.

For instance, while Yelp’s revenue grew from \$3.75 million in 2007 to over \$1 billion in 2019, 2020 saw a drop in revenue to \$872.9 million. The coronavirus pandemic severely impacted Yelp’s exponential growth curve since it mainly focuses on local businesses that require the physical presence of customers to succeed. With lockdowns and social distancing rules, these businesses couldn’t function normally for a long time.

Additionally, Yelp’s growth relied on user-generated content and the peculiar power of Google backlinks. However, Google has adjusted its algorithm to prevent backlink quantity from producing exponential returns, so this approach would no longer work.

This example demonstrates that you should adapt your path toward hitting exponential growth depending on the tools, tactics, and strategies available.

## Better understand your customer growth with Amplitude

In your quest for user acquisition, implementing strategies to promote exponential growth can be a powerful force multiplier. But, understanding your current product experience and user behavior is a critical first step.

With Amplitude, you can gain insights to make smarter, data-driven decisions to help fuel exponential growth. Easily visualize trends in your customer data and run analyses to improve your bottom line.

Julia Dillon
Senior Product Marketing Manager, Amplitude
Julia is a product marketer at Amplitude, focusing on go-to-market solutions for enterprise customers.

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