Tammy Todd

2021-08-11

Moore’s law states that the maximum number of transistors that can fit on a silicon chip doubles every two years.

The function$f\left(x\right)=42{\left(1.41\right)}^{x}$

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?

The function

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

Skilled2021-08-12Added 91 answers

1.$f(x)=42(1.41)$

2.$1000=42{\left(1.41\right)}^{x}$

$x={\mathrm{log}}_{1.41}\left(\frac{1000}{42}\right)$

$x=9.2264$

Set $f(x)=1000$ , which is 1 billion in the units we're using, and use fundamental features of logarithms to find the number of years x.

${\mathrm{log}}_{a}\left(b\right)=x<\to {a}^{x}=b$

3. x is the number of years since 2000. Since x is fractional we round up and add 2000 x=10, 2010 year.

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