What is the formula used to calculate popularity rating over time?

Question

Ratings

Hello, I will describe the task on the example of news:
Goal: you need to show the hottest news.
Input data: opening time and previous rating value
Output data: number
Conditions: store the current rating in the same table as the object itself (selection based on sorting), it is impossible (for example) to go through all records every day and artificially lower the rating so that new the records had time to "fly up"
The same in other words:
It is necessary that the frequently requested objects for the last week were higher than the objects that were very frequently requested six months ago. (like requests for iphone 6 and iphone 7)
The number of requests themselves is small for the same object, a simple incremental counter could be dispensed with, but popularity over time must be taken into account, and it is highly undesirable to use other tables for constant counting.