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 |
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