> For the complete documentation index, see [llms.txt](https://docs.collection.xyz/guides/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.collection.xyz/guides/technical-reference/bonding-curves/how-are-the-parameters-used-in-each-of-the-bonding-curves.md).

# How are the parameters used in each of the bonding curves?

<table><thead><tr><th width="130"></th><th>Linear</th><th>Exponential</th><th>Sigmoid</th></tr></thead><tbody><tr><td>Delta (uint128)</td><td><ul><li>The additive amount that the next price will increase/decrease by</li><li>No constraints</li></ul></td><td><ul><li>The multiplicative amount that the next price will increase or decrease by</li><li>1e18 represents 100%. If it increases by 20%, we need to put 1.2e18 as delta</li><li>Constrained to be ≥ 1e18</li></ul></td><td><ul><li>Represents the speed which <code>P_min</code> and <code>P_max</code> are attained. Low = slow, high = fast</li><li><code>delta</code> must be <code>k * 2**10</code> as a uint128. The value of k is normalized because most useful curves have k between 0 and 8, with small changes to k (e.g. 1/128) producing significant changes to the curve</li></ul></td></tr><tr><td>SpotPrice (uint128)</td><td><p>Ex-fees and royalties,</p><p>Bid | Ask ~= spotPrice | spotPrice + delta</p></td><td><p>Ex-fees and royalties,</p><p>Bid | Ask ~= spotPrice | (spotPrice * delta/ 1e18)</p></td><td>Not used</td></tr><tr><td>Props (bytes)</td><td>Not used</td><td>Not used</td><td><p>Represents an encoding of upper and lower bounds P_max and P_min </p><p><code>abi.encode(uint256(P_min), uint256(P_max - P_min))</code></p></td></tr><tr><td>State (bytes)</td><td>Not used</td><td>Not used</td><td><p>Represents where we are from the curve initialization point to calculate the right gradient</p><p></p><p><code>abi.encode(int128(n - n0))</code></p></td></tr></tbody></table>


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## 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, and the optional `goal` query parameter:

```
GET https://docs.collection.xyz/guides/technical-reference/bonding-curves/how-are-the-parameters-used-in-each-of-the-bonding-curves.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

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.