Implement exponential decay function in Solidity - ethereum

Question

I am working on an ERC-721 token in which there is a built-in royalty feature, i.e., when a user issues a token, he chooses the royalty fee in ETH and he is entitled to that fee on every secondary market trade. Also, the more tokens a user holds belonging to a specific issuer, the lower the royalty fees and I need to implement an exponential decay function to calculate the discount.
M = e ^ (-x / 50)
where, e is Euler's number
so the discountedFee = M * standardFee
For instance, the royalty fee of a token is 0.01 ETH and in the contract, it will be represented as 10000000000000000 WEI. Now the buyer holds 10 tokens of that issuer and now he is about to buy his 11th token, so the royalty fee will be calculated as
M = e ^ (-10 / 50) = 0.818
discountedFee = M * standardFee = 0.0081 ETH
Can this function in Solidity? Thanks in advance.

Answer 1

Implementing a true exponential decay in solidity is pretty difficult, let alone expensive since the language doesn't support floating point arithmetic. This link might be helpful.
Personally, I approximate an exponential decay with a series of linear functions targeting a half-life in a certain time-period.
function getPrice(uint256 value, uint256 t, uint256 halfLife) public pure returns (uint256 price) {
value >>= (t / halfLife);
t %= halfLife;
price = value - value * t / halfLife / 2;
}
Half-life in my code was the number of seconds in two days.