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Is Doubling Exponential?


Date: 17 Jul 1995 02:04:30 -0400
From: Jim W. Fox
Subject: MATH question

Several years ago, Gordon Moore, founder and chairman of Intel, made the 
following observation:

The logic density of silicon integrated circuits has closely followed the curve 
(bits per square inch)  = 2^{(n - 1962)}; that is, the amount of information 
storable in one square inch of silicon has roughly doubled yearly every year 
since the technology was invented.'

This has been interpreted to mean that the  power of computers will double 
every 12 - 18 months.  Many authors have written articles about this 
"exponential growth rate."

My question:

Is doubling exponential growth??  It seems to me that if computer power was 
being squared or raised to the power of 2 then this is exponential but simple 
doubling is not exponential.

What is the actual math definition??


Date: 17 Jul 1995 11:53:40 -0400
From: Dr. Ken
Subject: Re: MATH question

Hello there!

Yes, the function 2^(n-1962) is an example of an exponential function.  If a
quantity is well-modeled by an exponential function, it is said to exhibit
exponential growth.  

Exponential functions are based on the function e^x, where e is about 2.7.
They are called exponential functions because the variable is in the
exponent.  Note that the function 2^(n-1962) equals the function
e^(log[2^(n-1962)]) = e^(log[2]*(n-1962)).  So they're really only off from
each other by a constant.

Hope this helps!

-K
    
Associated Topics:
High School Exponents

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