# Orange Points

Orange Points is a rewards mechanism designed to incentivize OrangeLayer participants through a dynamic and equitable staking rewards system. By leveraging a non-linear decay formula, OrangeLayer aims to reward early stakers generously while ensuring long-term contributors are also rewarded appropriately. This document outlines the parameters and examples illustrating the potential rewards across various staking profiles.

### Reward Calculation Mechanism

The system utilizes a non-linear decay model to calculate rewards, offering a compelling incentive structure that balances early engagement with sustained participation.

#### Revised Parameters

**Staked Amount (S)**: The quantity of BTC staked by the participant.**Staking Duration (**$T$**)**: The total time the BTC is staked, measured in hours.**Base Reward Rate (**$R$**)**: Set at 100 points per BTC per hour, adjusting the reward potential upwards.**Decay Parameter (**$D$**):**It remains at 0.00001, controlling the reward rate's decrease over time.

#### Reward Rate Function

The hourly reward rate function is defined as:

$\displaystyle\huge f(S) = R * e^{-D . T^2}$

#### Total Rewards Calculation

Total OrangePoints earned over a staking period are determined by integrating the hourly reward rate from the start to the end of the staking period:

$\displaystyle\huge Total Points = S⋅\int_0^T R⋅e ^{−D⋅T ^2} dT$

### Example Scenarios

The following scenarios demonstrate the total OrangePoints for staking amounts ranging from micro to large investments under the revised reward rate:

**0.0001 BTC for 10 hours:**0.1 points**0.001 BTC for 100 hours:**9.68 points**0.01 BTC for 500 hours:**273.15 points**0.1 BTC for 1000 hours:**2802.47 points**1 BTC for 2000 hours:**28024.96 points**10 BTC for 10 hours:**9996.67 points**50 BTC for 100 hours:**483821.66 points**100 BTC for 500 hours:**2731459.86 points**150 BTC for 1000 hours:**4203710.86 points**200 BTC for 2000 hours:**5604991.22 points

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