Chapter 8.6, Problem 51SR

a.

To determine

To write the expression for the speed after $x$ years.

Answer to Problem 51SR

  $s\cdot 4^x$

Explanation of Solution

Given:

The computation speed has multiplied by a factor of $4$ about three years.

Calculation:

After $x$ , 3-year periods the computational speed increases by a factor of:

  $4^{\frac{3x}{3}}=4^x$

If the current computational speed is $s$ , the computational speed after $x$ , a 3-year period is given by:

  $=s\cdot 4^x$

b.

To determine

To find how long you wait to buy such a computer.

Answer to Problem 51SR

  $1.5$ Years.

Explanation of Solution

Given:

The computation speed has multiplied by a factor of $4$ about three years.

Calculation:

Let it is needed to wait for $x$ , 3-year periods, then:

  $\begin{array}{l}{s}_{new}=s\cdot 4^x\\ 5.6=(2.8)\cdot 4^x\\ 4^x=\frac{5.6}{2.8}\\ 4^x=2\\ x=\frac{1}{2}\end{array}$

So, it is needed to wait for $\frac{1}{2}$ three - year periods or $1.5$ Years.