Bonding Curve: y = ax^n+b

How does this bonding curve work?

The formula y = ax^n + b defines a polynomial bonding curve where the token price increases at a non-linear rate as more tokens are bought. Here, x represents the current token supply, a controls how fast the price grows, n determines the shape of the curve, and b is the base price.

When x is small, the price is close to b, meaning early buyers can purchase tokens cheaply. As more tokens are minted and x increases, the price rises faster over time, especially when n > 1, causing the curve to become steeper.

Unlike linear curves, the price does not increase at a constant rate — it accelerates, making later tokens significantly more expensive than earlier ones.

This creates a strong incentive for early buyers, as they can enter at much lower prices before the curve steepens.

Advantages and limitations

One of the main advantages of this model is its flexibility. By adjusting a and n, developers can control how aggressive or smooth the price growth is, making it suitable for different types of token economies.

It can create a more dynamic pricing experience compared to linear models, allowing for stronger early incentives and more noticeable progression.

However, the curve can become very steep at higher supply levels, especially with larger n, making tokens expensive quickly and reducing accessibility for late buyers.

Additionally, like other bonding curves, the price is purely formula-based and does not reflect real market demand, which can lead to mispricing.