my question is about exponential decay and its factor.
English isn't my native language and therefore I'm not sure about the precise definition in my particular case.
I'm reading a specific paper and here it is described, not so well, an algorithm. The part I'm not sure about is as follow: I have a x variable of value 1e-7, this algorithm has a loop and it is said that after every 10 iterations it is applied to x "an exponential decay with decay factor 0.95".
Do you think the correct interpretation would be to multiply the actual x value for $e^{-0.95}$ at each step that the update is required? As wikipedia states, the $\lambda$ is called constant and not factor
Another option could be for me to multiply by 0.95 and not $e^{-0.95}$
I'm sorry if my question is dumb but I can't verify the answer with brute force and I think this is the best place to find the most accurate one
If you have an exponential decay of $5\%$ after 10 steps then the equation is
$$e^{-\lambda x}=e^{-\lambda 10}=0.95\Rightarrow \lambda=\frac{-\ln(0.95)}{10}\approx 0.00512933$$
If we have an inital value of $5$ then after 10 steps we have $y(10)=5\cdot e^{-0.00512933\cdot 10}=4.75=5\cdot 0.95$
This is what we wanted. For a reference see here.
Here is a graph with the initial value $5$. You see that the decay is not linear.