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A math exercise of sorts, not work, not school, just some idea I have rolling in my head that I'm trying to get a concrete answer for.

A revolutionary item was introduced in 1990, first of its kind. There were 111 similar/copycat items produced until 2011 when the next revolutionary item in its class was introduced. That would be 5.3 items/year for 21 year between 1990 and 2011.

Others further caught on and even more copycats came onto the scene so between the years 2011 and 2022, 24.5 items per years were produced. BUT the next revolutionary item has yet to come.

Based on these numbers, can you predict what year the next revolutionary item was/is supposed to be introduced in terms of year?

Currently, I only have a simple arithmetic of:

  • 24.5/5.3=3.7 as the rate increase
  • 21 years between the first two so 21/3.7=4.5 years
  • 2022+4.5=2026 as the next year the revolutionary item would be produced.

BUT, if I were to calculate for say, 2014, it would be (assuming same 24.5 rate):

  • same: 24.5/5.3=3.7 as the rate increase
  • same: 21 years between the first two so 21/3.7=4.5 years
  • 2014+4.5=2018, which just doesn't seem right.

What am I missing here? Is it possible to figure this out with the data points provided? Just driving me nuts trying to do the maths on this.. thanks in advance.

Darren
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  • You do not provide a model. What affects the probability to get the next item? Maybe the model says that since there are so many copycats, the drive to innovate is no longer there, and the one willing to produce the next revolutionary item just gave up. – Andrei Jul 01 '22 at 20:16
  • "What affects the probability to get the next item?" That's a good question and I don't really know how to answer that question. Also, let's assume the drive to innovate will always be there. This isn't a problem from a book or anywhere. I just have a table of data and I'm just trying to see if it would be possible to predict with the data available. – Darren Jul 01 '22 at 21:32
  • You are trying to draw a curve using two points. But you don't know what curve to draw. So then the answer is no, you can't predict. – Andrei Jul 02 '22 at 02:19

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