Q65. - Algebra 2

Question

If a typical computer operates with a computational speed s today, write an expression for the speed at which you can expect an equivalent computer to operate after x three-year periods.

Step-by-Step Solution

Answer

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

Step 1. Given Information.

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.

Step 2. Explanation .

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:

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

Step 3. Conclusion .

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