How can I accurately depreciate a set of elements? I have the following function to determine the value $v$ of an element: $$a =\space\text{age in days} \\\ v = a\left(\frac{-1}{730}\right)^\frac{5}{8} + 1$$ My intention is for each element, which starts out with a value of $1$ at the moment of its creation, to depreciate in value daily at a declining rate. But it turns out that it would be too costly in terms of computing power to calculate each element individually. So, instead, I would like to consolidate the calculation into one variable $t$, which will increase by 1 each time an element is added. Then every day, $t$ will be multiplied by a certain value $r$ (probably around $0.99$) to depreciate it. Is there a value I can choose for $r$ to make the depreciation rate match the rate in my original function?

If my reading $v=1-a\left(\frac{1}{730}\right)^\frac{5}{8}$ is correct, the item is linearly depreciated to zero value in about $61.6$ days and the value goes negative after that. You should throw them away. Then you can just store the number of items added each day for the last $61$ days. If $n(i)$ is the number added $i$ days ago, the total value is then $\sum n(i)(1-\frac i{61.6})$

Your suggestion to use a multiplier will result in things always having positive value. I don't know which suits your reality better.