Chapter 7.1, Problem 27E

To determine

To Find:The equation that gives $c$ as a function of $A$ . Then find the number if chips per wafer when the area of the chip is $81$ square millimeter.

Answer to Problem 27E

  $c=\frac{a}{A}$ , $320$

Explanation of Solution

Given:

  

From the given table it is seen that as the area increases the number of chips decreases.

i.e.

It shows inverse variation

We know thatEquation for inverse variation: $xy=a,y=\frac{a}{x}$

Then

The equation that gives $c$ as a function of $A$ is $c=\frac{a}{A}$

Now we have to find the number if chips per wafer when the area of the chip is $81$ square millimeter.

Put $A=58,c=448$

  $\begin{array}{l}c=\frac{a}{A}\\ 448=\frac{a}{58}\\ a=25984\end{array}$

Substitute $a=25984$ in inverse variation equation when $A=81$

Thus

  $\begin{array}{l}c=\frac{25984}{81}\approx 320\\ c\approx 320\end{array}$

Hence, $320$ chips per wafer when the area of the chip is $81$ square millimeter.