# Reward Pool Drip Models

The drip model for a reward pool defines the rate at which assets deposited into the reward pool accrue (i.e. "drip") to stakers. 

Drip models must conform to the `IDripModel` interface, and may use a reward pool's last drip time to determine the returned drip factor. 

```solidity
interface IDripModel {
  /// @notice Returns the drip factor, the percentage of undripped rewards which should drip to stakers, as a wad. For
  /// example, it there are 100 undripped reward assets and this method returns 1e17, then 100 * 1e17 / 1e18 = 10 assets
  /// will drip.
  /// @param lastDripTime_ Timestamp of the last drip
  function dripFactor(uint256 lastDripTime_) external view returns (uint256 dripFactor_);
}
```

The drip model gets specified in the `RewardPoolConfig` struct when a config is passed during Rewards Manager deployment or update (see [Define Rewards Manager Configuration](https://csm-docs.cozy.finance/developer-guides/create-a-rewards-manager/define-a-rewards-manager-configuration)). Note the drip model can differ for each individual reward pool.

For details on how exactly rewards drip works, check [here](https://csm-docs.cozy.finance/rewards-manager-accounting#when-do-rewards-drip).

### Exponential-rate drip model

A default exponential-rate drip model implemented in [`DripModelExponential`](https://github.com/Cozy-Finance/cozy-safety-module-models/blob/main/src/DripModelExponential.sol).

The drip rate is a fixed number, `uint256 public immutable ratePerSecond`. In this model, rewards drip according to the exponential decay function `A = U * (1 - r)^t`, where:

* *U* is the starting amount of undripped rewards
* *A* is the remaining amount of undripped rewards after some number of seconds
* *t* is the number of elapsed seconds
* *r* is the per-second drip rate

From some simple math, we can compute the *r* value for a desired rate of drip. 

Suppose you want to drip 25% of rewards per year. You then make the following substitutions:

* U is `1`, or 100%, since we don't care what the actual starting value is, only what it decays to.
* *A* is `0.75` because the desired drip rate is 25%, and 100% reduced by 25% is 75%.
* *t* is `31557600`, the number of seconds in a year. The time period is arbitrary. We use a year only because our target rate is 25% drip *per year*.

This results in the following formula:

> 0.75 = 1 \* (1 - r ) ^ 31557600

We may now solve for *r* as follows:

> 0.75 = 1 \* (1 - r ) ^ 31557600\
> 0.75 = (1 - r ) ^ 31557600\
> 0.75 ^ (1 / 31557600) = 1 - r\
> 0.75 ^ (1 / 31557600) - 1 = - r\
> r = -((0.75 ^ (1 / 31557600)) - 1)\
> r = 0.000000009...

Finally, we can multiply *r* by a wad to get `ratePerSecond` is approximately `9e9`.

#### Deploying a exponential-rate drip model

If you would like to deploy the exponential-rate drip model and use it for reward pools in the Rewards Manager, you can use the dedicated [`DripModelExponentialFactory`](https://github.com/Cozy-Finance/cozy-safety-module-models/blob/main/src/DripModelExponentialFactory.sol).

To deploy the model, call the following function on that factory:

```solidity
/// @notice Deploys a DripModelExponential contract and emits a DeployedDripModelExponential event that
/// indicates what the params from the deployment are. This address is then cached inside the
/// isDeployed mapping.
/// @return model_ which has an address that is deterministic with the input ratePerSecond_.
function deployModel(uint256 ratePerSecond_) external returns (DripModelExponential model_);
```

Because the `deployModel` function is deterministic, it will revert if a model with your desired configurations already exists. To first confirm that your model needs to be deployed, you can call the `getModel` function with the same params you would pass to `deployModel`. The `getModel` function will return the address of the model that has your desired configs, if one exists.

The most up-to-date instructions on how to use the factory can be found in its [source code](https://github.com/Cozy-Finance/cozy-models-v2/blob/main/src/DripDecayModelConstantFactory.sol).

For the addresses of factories deployed to various chains, see our [contracts deployments registry](https://csm-docs.cozy.finance/developer-guides/contract-deployments-registry).