In one sentence
High-growth companies usually do not grow exponentially for long. Their growth is better understood as overlapping campaign, product, geographic, and market-adoption curves—typically logistic or “Elephant Curves”—whose combination produces approximately quadratic growth. This model leads to better forecasting and more practical growth decisions.
Overview
Cohen begins by separating exponential growth—constant percentage growth—from quadratic growth, where the absolute increment increases by roughly a constant amount. He argues that public growth charts for Facebook, Slack, Dropbox, Trello, Lyft, and HubSpot do not show sustained exponential behavior. HubSpot, for example, had declining percentage growth but increasingly large absolute annual revenue additions, which fits a quadratic curve better.
His central mechanism is the “Elephant Curve” of a growth initiative: a campaign or product starts slowly, accelerates as the team discovers effective positioning, reaches an optimization phase with roughly steady contribution, and eventually declines as audiences saturate, channels weaken, or acquisition becomes uneconomical. Stacking many such curves creates “wavy quadratic” company growth. The same pattern applies to product lines and geographies.
Cohen treats virality, word-of-mouth, and hot trends differently. Their underlying mechanisms can be exponential initially, but finite markets and increasingly difficult customers impose a carrying capacity. Logistic growth—early acceleration, a roughly linear middle, and eventual flattening—is therefore more realistic. When multiple logistic curves begin at different times and have different limits, their aggregate again resembles quadratic growth.
Core ideas
Do not confuse CAGR with the actual growth process
A constant CAGR describes an exponential curve, but matching a beginning and ending value with a CAGR does not prove that the company grew by that percentage every year. Examine absolute year-over-year additions as well as percentage growth.
The Elephant Curve is a reusable growth pattern
Most initiatives move through four phases: ineffective launch, rapid improvement, a sustained optimization plateau, and decline. Decline may come from audience saturation, channel deterioration, or rising auction prices—not necessarily from poor execution.
Stacked initiatives create quadratic-looking growth
Once campaigns, products, or regions reach their productive middle phase, each contributes something roughly linear. Adding more linear contributors over time produces an overall curve that looks quadratic, often with waves when new initiatives launch.
Virality is usually logistic in the real world
A viral loop may be exponential while the reachable market is far away. As adoption approaches the market’s carrying capacity, remaining prospects become harder to convert and growth passes through a linear phase before flattening.
Market size and market share should be modeled separately
A company can appear to grow linearly because it is saturated in mature markets while still expanding in newer ones. Track total market growth, product market share, and monetization per customer as distinct curves.
Revenue can grow faster than users without exponential user growth
Revenue equals customers or usage multiplied by revenue per customer. If both components rise in an Elephant-like or roughly linear way, their product can look quadratic. Pricing, usage intensity, and monetization can therefore extend growth after user growth slows.
Growth decay is often structural
Declining percentage growth is not automatically evidence of a failing business. A company adding increasingly large absolute amounts can still show lower percentages as its base expands; the correct question is which underlying component has changed.
At scale, new growth usually requires a new curve
Features may improve an existing curve, but substantial renewed growth generally requires a new product, geography, sales mechanism, pricing model, or market. A second product is unlikely to match the first, so sustained hypergrowth requires multiple bets and willingness to kill weak ones.
Practical takeaways
- Forecast growth by component: total market, product market share, and revenue per customer; multiply the forecasts rather than applying one headline growth rate.
- For every campaign, estimate its phase: launch, acceleration, optimization, or decline. Budget and targets should reflect that phase.
- Measure absolute additions—new customers, dollars, or users—not only percentage growth.
- When a channel plateaus, determine whether the problem is creative optimization, inventory saturation, audience exhaustion, or uneconomical pricing.
- Start new channels before the current channel visibly collapses; successful initiatives take time to discover and scale.
- Decide whether to pursue one large new growth avenue or many smaller campaigns based on expected scale, efficiency, and concentration risk.
- For mature products, prioritize initiatives that enlarge the carrying capacity: new markets, major product changes, new geographies, or built-in word-of-mouth.
- Distinguish viral, word-of-mouth, and trend-driven adoption. They have different mechanisms even though all can produce rapid early growth.
Caveats and counterpoints
- The quadratic claim is a broad empirical model, not a universal law. Cohen acknowledges that the data are especially visible for companies publicly presenting runaway growth and that low-growth companies may behave differently.
- Several charts and comparisons rely on publicly available presentations or secondary sources; the fit of a curve can depend on the chosen time window, metric, and visual scale.
- “Quadratic” describes the aggregate shape, not necessarily the causal mechanism of every company. Regulatory shocks, competition, pricing changes, acquisitions, and operational constraints can disrupt the pattern.
- A logistic model assumes a meaningful carrying capacity. That capacity can move because markets expand, new use cases appear, prices fall, or the product changes, making saturation difficult to estimate.
- The article’s examples and forecasts are from an essay published March 5, 2022; some referenced company trajectories later changed. The enduring value is the modeling framework, not every numerical illustration.
Questions worth revisiting
- For the business I am analyzing, what is the true unit of growth: paying customers, active users, usage, revenue, or gross profit?
- Which current growth initiatives are in launch, optimization, or decline—and what evidence supports that classification?
- What is the carrying capacity of the present market, and what could expand it?
- Are declining percentages masking increasing absolute additions, or are both measures deteriorating?
- Would a new product, geography, pricing model, or distribution channel create a genuinely new Elephant Curve?
- How much of growth comes from market expansion versus gaining share within an existing market?
- What would have to be true for an apparently viral mechanism to remain exponential rather than become logistic?
Return to this when…
Return to this essay when a team uses “exponential,” “hypergrowth,” or a constant CAGR as if it were an operating explanation. Revisit the Elephant Curve and component-modeling sections before making growth forecasts, setting marketing budgets, interpreting growth decay, or deciding whether a mature product needs a new market or product.