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Appendixes

# Appendix 1. Yield farming mathematical model.

The amount of tokens allocated to Yield Farming rewards is 64.000.000. The token releasing for farming follows a linear function in order to offer good rewards to the farmers during all 36 months.
If rewards were a constant amount, farmers will have huge rewards at the beginning and very low rewards at the end of the farming phase (due to the amount of tokens in circulation). This way, we are rewarding farmers with very interesting amounts from day one until the end of the farming phase.
Taking 1 month as unit...
Releasing is defined by a straight line function:
Where rewards in a certain period of time are defined by the integration of the function above:
As we know, from month 0 to 36, 64.000.000 TUT will be released. Assuming B is zero because if no time has passed no tokens are released (obviously):
$\int _{0} ^{36} (Ax) dx = 64.000.000$
$A = \frac {(64.000.000)(2)} {(36)^2} = 98.765,4321$
The straight line function that defines the growth of rewards releasing is:
$y = 98.765,4321x$
And rewards are calculated by the integration of the function above in a certain period of time:
$Rw = \int _{t_0} ^{t_1} (98.765,4321x) dx$
Farmers are allowed to claim their rewards, according to the function above, the ratio (R) and the participation (P):
$Rw = \int _{t_0} ^{t_1} ((98.765,4321x)(P)(R)) dx$
E.g. A token holder is providing 50.000 TUT (and 0,07 BTC) as liquidity to the pool and staking their LP tokens in Tutellus since first of month 12 and he is claiming for their rewards at the first of month 14. His liquidity represents 5% of the pool. There is a ratio of 4:1 in LP/FC2, meaning LP gets 80% of rewards against 20% for FC2. Assuming none of these ratios change through this period, rewards are calculated in this way:
$Rw = \int _{12} ^{14} ((98.765,4321x)(0,05)(0,8)) dx = 7.901,23{\space} TUT$
$APR = \frac {7.901,23}{50.000} · \frac{12}{2} = 95\%$
This represents 95% APR for that period. This might vary if any of the ratios change. If liquidity of the pool is duplicated, rewards will be half of those calculated, for example.