Chapter 4.3, Problem 14PPE

To determine

Rule that represent the function of given ordered pairs, $\left(1,\frac{2}{3}\right),\left(2,\frac{4}{9}\right),\left(3,\frac{8}{27}\right),\left(4,\frac{16}{91}\right),\left(5,\frac{32}{243}\right)$

Answer to Problem 14PPE

The rule of the function is $y={\left(\frac{2}{3}\right)}^x$

Explanation of Solution

Given:

The given ordered pair is,

  $\left(1,\frac{2}{3}\right),\left(2,\frac{4}{9}\right),\left(3,\frac{8}{27}\right),\left(4,\frac{16}{91}\right),\left(5,\frac{32}{243}\right)$

First represent the given ordered pair in a tabular form.

x	1	2	3	4	5
y	2/3	4/9	8/27	16/81	32/243

Now, for first column

For x = 1, y = 2/3

It can be represented by the rule $y={\left(\frac{2}{3}\right)}^x$ only.

Now, checking this rule for second column

Putx = 2

  $\begin{array}{l}y={\left(\frac{2}{3}\right)}^2\\ =\frac{4}{9}\end{array}$

So it is same for second column.

Similarly, it is same for the remaining column also.

Hence, the rule of the function for the given ordered pair is $y={\left(\frac{2}{3}\right)}^x$