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)x models 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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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)x  models 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?

Sally Cresswell · Accepted Answer

1.f(x)=42(1.41)2.1000=42(1.41)xx=log1.41(100042)x=9.2264Set&amp;nbsp;f(x)=1000&amp;nbsp;, which is 1 billion in the units we&#039;re using, and use fundamental features of logarithms to find the number of years x.loga(b)=x&amp;lt;→ax=b3. x is the number of years since 2000. Since x is fractional we round up and add 2000 x=10, 2010 year.

Moore’s law states that the maximum number of transistors that can fit

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