Suppose your computer operates with a processor speed of 600 megahertz and you want a computer that can operate at 4800 megahertz. If a computer with that speed is currently unavailable for home use, how long can you expect to wait until you can buy such a computer?

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

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

Suppose a computer operates with a processor speed of 600 megahertz and a computer that can operate at 4800 megahertz is to be bought. The number of years to be waited to purchase such a computer is to be determined.

Since the required speed is 4800 megahertz, $y=4800$

And the present speed is 600 megahertz, $s=600$

Plugging the values in the equation:

$\begin{array}{l}y=s{\left(4\right)}^{\frac{t}{3}}\\ 4800=600{\left(4\right)}^{\frac{t}{3}}\\ {\left(4\right)}^{\frac{t}{3}}=\frac{4800}{600}\\ {\left(4\right)}^{\frac{t}{3}}=8\\ {\left(2\right)}^{\frac{2t}{3}}=2^3\\ \frac{2t}{3}=3\\ 2t=9\\ t=\frac{9}{2}\\ t=4.5\end{array}$

Hence the number of years to be waited to purchase such a computer is 4.5 years.