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DareDeveloper

Formula for Exponential Growth

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Hi all,

 

I have been algebra free for probably a decade.

Yesterday I thought I wanted to accomplish something easy: finding a function that describes the growth shown in this image:

http://en.wikipedia.org/wiki/The_Singularity_Is_Near#mediaviewer/File:PPTExponentialGrowthof_Computing.jpg

 

I did not really get anywhere ... and my colleagues say it is a case for letting a math program determine the function through ... dunno ... something with regression!?

 

I thought it should not be too hard to calculate the function, but maybe I am wrong!?

 

What I think I remember tells me that I could write a function that describes how the slope changes ... and then use integral stuff somehow to get the actual function (the antiderivative?).

Or is it possible to use given information from the image to choose values to build an exponential function directly?

Or are my colleagues right? Is it not trivial?

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It's exponent with certain scaling on both axes.

Red dots represent computing power which follows Moore's Law (x2 every 2 years).

e^x also has similar shape.

 

I think you're overcomplicating problem by trying to create function based on data instead of making a guess based on visual information.

Not to mention you have no accurate data to begin with.

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Thanks for responding.

 

I started by guessing and trying to get something that comes close with the google search math graphs ...

but I need to understand what I am doing to get anywhere near that graph.

 

I wanted to figure out how much of a difference the fact that the progress is getting faster makes ...

but I have not managed to formulate the linear function that estimates the values for the 2000 - 2050 range either.

 

I am really rusty unsure.png

Edited by DareDeveloper

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Looks about correct:

[attachment=24136:untitled.png]

 

Formula:

y = 10 ^ (2 ^ ((x - 1900) / 2 / 28) * (70 / 12) - 10)

Where x is 1900 to 2100.

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