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Not sure if this is the right place(If not, where?) to ask this, but I am trying to come up with a formula based on a scenario.

There is a website where users can pay to get a certain amount of "Downloads" per month. The max amount of downloads is 200 for the basic plan. The user can upgrade their plan to get more downloads.

A message is sent to the user when they reach 75% of their max downloads informing them they might want to upgrade their plan. For example, 150 downloads are reached(in a specific month) a message is sent.

The formula part:

So I want to figure out the potential missed days amount if the user does not upgrade. So I need to figure out how many days they have remaining based on how long it took to get to 75% of their max downloads.

Sample numbers: Month of August. On August 16th, the user reached 75% of their max downloads. There are 15 days left in August and 31 days total.

Not sure if this makes sense. Thank you.

Etra
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If it takes $d$ days to reach $75\%$ then (assuming a standard daily download rate) the rate is $25\%$ every $d/3$ days. So they will use up their quota in another $d/3$ days.

In your example, $d=16$ days so they will run out in about $5$ more days, on August 21.

Ethan Bolker
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Is this summary correct?: Based on the user's usage rate, their download limit will be reached on approximately Aug $21,$ so for this month, they will be missing $10$ days out of $31.$

If so, let $x$ be the day of the month on which they reach the $75\%$ quota, and $y$ be the number of days in that month. Then the number of “missed days” is expected to be $$\frac{3y-4x}{3}.$$

$=9.67\textrm{ days}$, in our example.

This formula returns a non-positive number of “missed days” when the user, because their usage for the month has been within the plan rate, is not being expected to exceed their download limit this month. So, the system ought to be set up to trigger the upgrade-suggestion message only if the value is positive.

ryang
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  • Maybe this is a stupid question, but what if the 75% of the downloads were reached on August 25th instead of August 16th? This would make the result negative. – Etra Aug 30 '21 at 21:33
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    @Etra Good question! I've expanded the answer to address it. – ryang Aug 30 '21 at 21:48
  • Appreciate it. That is what I was going to do but wanted to make sure. Thanks again. – Etra Aug 30 '21 at 21:50