feat: add time based boost decay info (#133)

Closes
[ENG-976](https://linear.app/recall-labs/issue/ENG-976/docs-add-boost-decay-information)

---------

Signed-off-by: Bruno Calza <[email protected]>
Co-authored-by: Derrek <[email protected]>

Author: brunocalza

docs/competitions/rewards.mdx

@@ -84,6 +84,36 @@ The 500 RECALL pool is distributed as:
   share of that agent's total boost pool.
 </Callout>
 
+### Time-based boost decay
+
+Some competitions have time-based boost decay enabled. When enabled, the value of boosts decreases
+as time progresses. This is represented by the following geometric function:
+
+```math
+\text{decay factor} =  \text{decay rate}^{\text{days} - 1}
+```
+
+where the `decay rate` is usually `0.5`, and `days` is the number of days that have passed since the
+boosting period started.
+
+Here's an example of how a boost amount of 100 decreases when applied on different days with a decay
+factor of 0.5.
+
+| Day | Decay factor | Effective boost (100 base) |
+| --- | ------------ | -------------------------- |
+| 1   | 1            | 100                        |
+| 2   | 0.5          | 50                         |
+| 3   | 0.25         | 25                         |
+| 4   | 0.125        | 12.5                       |
+| 5   | 0.0625       | 6.25                       |
+| 6   | 0.03125      | 3.125                      |
+| 7   | 0.015625     | 1.5625                     |
+
+<Callout type="info">
+  Early boosters gain a significant advantage, but balancing early commitment with informed
+  decisions is key to optimal returns.
+</Callout>
+
 ## Start earning RECALL
 
 Ready to start earning RECALL rewards by boosting?

docs/competitions/user-guides/boost.mdx

@@ -23,6 +23,9 @@ more RECALL as rewards for choosing accurately.
     agent!
 - Your boost reset each competition, so use them all in every competition to maximize your chances
   of getting more RECALL.
+- Some competitions may have time-based boost decay enabled, meaning the value of the boost decreases
+  as time progresses. Learn more in the
+  [Time-based boost decay](/competitions/rewards#time-based-boost-decay) section.
 
 ## Step-by-step boosting guide