Parameters for Exponential Curve
Last updated
Last updated
If exponential curve is chosen to establish the relationship between the price of tokens and the supply of tokens, then:
Parameter | Meaning |
---|---|
The function provided allows for the calculation of the correlation between Anchor Token TVL and the Token Supply:
Anchor tokens pertain to the tokens utilized for minting or purchasing project tokens, such as ETH or USDC.
Anchored Token TVL denotes the cumulative value of anchored tokens secured within the Bonding Curve contract.
In the context of defining the curve within Burve protocol, specifying the values of a and b is essential.
When the supply is 0īŧit follows that p=a. In this scenario, the value of a represents the initial price of the tokenīŧ
The A-value is defined as the Anchor Token TVL divided by the increase in token price over the initial price.
The specific value of the Anchor Token TVL is already known:
The increase in token price from the initial price is a multiple of:
Thus A-value isīŧ
When TVL is relatively large:
Then b-value is calculated with the Parameter A:
Parameter Setting Example:
If the project aims for an Initial Token Price of 0.01USDC and plans for the token price to surge by 100 times when the TVL reaches 1,000,000USDC, the following settings can be implemented:
Initial Token Price: 0.01 USDC
A-value: 100,000 (derived from A = 1,000,000 / 100)
In this configuration, the relationship between the supply of tokens, price, and TVL would adhere to the specified conditions:
The parameter b in the equation signifies the scaling on the X-axis for the function, which often lacks practical significance. To address this, the Burve Protocol introduces the parameter A as a replacement.
Supply | Price(USD) | TVL(USD) |
---|---|---|
100,000
0.01105159459
1,051.594593
200,000
0.0122137743
2,213.774304
300,000
0.0134981682
3,498.168205
400,000
0.01491762827
4,917.628274
500,000
0.016486358
6,486.357997
600,000
0.01822005449
8,220.054489
700,000
0.02013606557
10,136.06557
800,000
0.02225356333
12,253.56333
900,000
0.02459373602
14,593.73602
1,000,000
0.02718
17,180
1,100,000
0.0300382341
20,038.2341
1,200,000
0.03319703856
23,197.03856
1,300,000
0.03668802118
26,688.02118
1,400,000
0.04054611365
30,546.11365
1,500,000
0.04480992104
34,809.92104
1,600,000
0.0495221081
39,522.1081
1,700,000
0.05472982621
44,729.82621
1,800,000
0.06048518514
50,485.18514
1,900,000
0.0668457745
56,845.7745
2,000,000
0.07387524
63,875.24
2,100,000
0.08164392029
71,643.92029
2,200,000
0.0902295508
80,229.5508
2,300,000
0.09971804157
89,718.04157
2,400,000
0.1102043369
100,204.3369
2,500,000
0.1217933654
111,793.3654
2,600,000
0.1346010898
124,601.0898
2,700,000
0.1487556676
138,755.6676
2,800,000
0.1643987332
154,398.7332
2,900,000
0.1816868151
171,686.8151
3,000,000
0.2007929023
190,792.9023
3,100,000
0.2219081753
211,908.1753
3,200,000
0.2452439191
235,243.9191
3,300,000
0.271033637
261,033.637
3,400,000
0.2995353877
289,535.3877
3,500,000
0.3310343671
321,034.3671
3,600,000
0.3658457621
355,845.7621
3,700,000
0.4043179046
394,317.9046
3,800,000
0.4468357569
436,835.7569
3,900,000
0.4938247634
483,824.7634
4,000,000
0.5457551085
535,755.1085
4,100,000
0.6031464206
593,146.4206
4,200,000
0.666572972
656,572.972
4,300,000
0.7366694253
726,669.4253
4,400,000
0.8141371837
804,137.1837
4,500,000
0.8997514097
889,751.4097
4,600,000
0.9943687815
984,368.7815
4,700,000
1.098936065
1,088,936.065
4,800,000
1.214499587
1,204,499.587
4,900,000
1.342215707
1,332,215.707
5,000,000
1.483362385
1,473,362.385
5,100,000
1.639351971
1,629,351.971
5,200,000
1.811745338
1,801,745.338
p
Token Price
s
Token Supply
a
Parameter 1
b
Parameter 2