Moore's law states that the maximum number of transistors that can fit on a silicon chip doubles every two years. The function f (x) = 42 (1.41) to the X power model the number of transistors, in millions, that can fit on a chip, where X is the number of years since 2000. Using this model, in what year can a chip hold 1 billion transistors?

Question

Mathematics

Jolly

5 June, 04:24

Moore's law states that the maximum number of transistors that can fit on a silicon chip doubles every two years. The function f (x) = 42 (1.41) to the X power model the number of transistors, in millions, that can fit on a chip, where X is the number of years since 2000. Using this model, in what year can a chip hold 1 billion transistors?

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Kiera Orozco · Answer 1

This is the equation of compound interest where x is the number of years:

A=initial value x (1 + interest in %) ^x

in our case: 1,000,000,000 = 42 x (1+.41) ^x

You solve x either with a calculator or with logarithm & you will find 49.44 years or almost 50 years. So it will reach the billion in 2050

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