# Bonding Curve

## Token Allocation

* The total fungible tokens of the collection is fixed at 1B and the NFTs part amount is customized by the token creator.
* 800M fungible tokens are allocated in the bonding curve pool for sale to raise initial liquidity. 
* 200M fungible tokens are reserved for adding to the liquidity pool on DEX.\ <br>

## Parameters

<br>

<figure><img src="https://2263012936-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FpKN0eO8Z2GX6VWMKxhEN%2Fuploads%2FYFefxz3L1i3kKFK0dMwh%2FScreenshot%202024-10-21%20at%203.09.32%E2%80%AFPM.png?alt=media&#x26;token=4ca4ac20-afbe-4a6c-80dd-da275a076260" alt=""><figcaption></figcaption></figure>

### Equation:&#x20;

$$
P(x) = 4 \times 10^{-9} e^{\frac{x \ln{10}}{0.8 \times 10^9}}
$$

### Parameter Definitions:

* P(x)  is the token price in ETH
* X is the token supply, ranging from 0 to 800M

### Initial Conditions

* At token creation, the initial token price is 4\*10^(-9) ETH
* The initial market cap of the collection is 4ETH(initial token price\*1B).

### Graduation Conditions:

* At graduation(x=800M), the token price is 4\*10^(-8)ETH
* The total market cap of the collection is 40 ETH ( token price\*1B) .

### Total Raised Funds(TRF):

$$
TRF = \int\_0^{800M} 4 \times 10^{-9} e^{\frac{x \ln{10}}{0.8 \times 10^9}} , dx \approx 12.5 , ETH
$$

### Liquidity Pool on DEX Construction:

* Deposited ETH= TRF\*85% ≈ 10.625ETH
* Deposited Token=200M

### Price Increase When Depositing LP&#x20;

* Initial Price on DEX=Deposited ETH/Deposited Token ≈ 5.3125\*10^(-8)ETH
* Graduating Price on Bonding curve is 4\*10^(-8)ETH
* Thus, the token price on the DEX LP at the very start is \~32% higher compared to the graduation price on the bonding curve.