# Bonding Curves

#### How Apex Burst Bonding Curves Work

Similar to the **Liquidity Book** feature on Trader Joe, Apex Burst’s bonding curves use **bins** to hold token amounts and determine prices. When AVAX is exchanged for a token, tokens are distributed from a bin until it’s empty, then the process moves to the next available bin. Token prices increase by **20% per bin**, using a step-wise approach for a structured and incremental bonding curve.

This design allows **Apex Burst** to support multiple pricing strategies, offering flexibility for various token launches.

#### Curve Types Available on Apex Burst

On the **Create** page, Apex Burst provides several curve options:<br>

<figure><img src="/files/w4qopuMspEs7LjBdGum5" alt=""><figcaption></figcaption></figure>

1. **Linear Pricing**: Price increases linearly with supply. This curve offers predictable pricing where each additional token incrementally increases in cost.
2. **Carrying Capacity Curve (Logarithmic-like)**: Price rises quickly initially but levels off as supply increases. Early buyers face higher price increases, but later growth stabilizes, reducing further price jumps.
3. **Exponential Curve**: Price increases exponentially with supply. This curve rewards early participants, but prices escalate rapidly.
4. **Cubic Curve (Bell)**: Price increases rapidly at the start, consolidates in the middle, and rises again towards the end. This curve offers both early and late buyers opportunities, with a mid-point where prices stabilize.

#### Mathematical Formulas for Bonding Curves

**Price Calculation for Each Bin**

To calculate the price in each bin, the formula is:

$$
price = basePrice \times \left(1 + \frac{i \times x}{100}\right)
$$

Where `i` is the bin index (starting from 0), `basePrice` is the initial token price and `x` is the increment factor per bin.

**Calculating the Last Non-Zero Bin Price**

The price for the final bin with non-zero tokens is:

$$
{lastNonZeroPrice} = \text{basePrice} \times \left(1 + \frac{(n - 1) \times 20}{100}\right)
$$

Where `n` is the total number of bins and `x` is the increment factor. This helps determine the final bin price at the end of the distribution.

**Market Cap Calculation**

The market cap, representing the token’s final value on a DEX like Trader Joe, is calculated as:

$$
{requiredMarketCap} = \text{totalDistribution} \times \text{lastNonZeroPrice}
$$

**Fraction Validation**

To validate the fraction of total supply in the bins, use:

$$
{cumulativeValue} = \sum\_{i=0}^{n-1} \text{lists}\[i] \times \text{price}\_i
$$

Then, the fraction is calculated as:

$$
{fraction} = \frac{10,000 \times \text{requiredMarketCap}}{\text{cumulativeValue} + \text{requiredMarketCap}}
$$

This formula ensures the allocation aligns with the desired distribution on the bonding curve and the total selected amount required for bonding.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.apexdefi.xyz/burst/bonding-curves.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.