91Ó°ÊÓ

Given that since computers were invented, computational speed has multiplied by a factor of 4 about every three years.

If a typical computer operates with a computational speed s today, an expression for the speed at which an equivalent computer is expected to operate after x three-year periods is to be determined.

The computational speed multiplies by a factor of 4 every three years i.e., the exponential growth factor for every period is 4.

An exponential growth is of the form $y=a{b}^x$

The growth factor is b = 4.

And the period is of 3 years, so the exponent has a factor of 3.

Plugging the values in the equation:

$y=s{\left(4\right)}^{\frac{t}{3}}$

Hence an expression for the speed at which a typical computer that operates with a computational speed s today is expected to operate after x three-year periods is $y=s{\left(4\right)}^{\frac{t}{3}}$