Chapter 4.3, Problem 2P

To determine

The pattern is to be identified to complete the table.

Answer to Problem 2P

The complete table is,

x (number of figures)	y (number of new branches)
1	3
2	9
3	27
4	81
5	243

Explanation of Solution

The table shows the number of new branches in each figure of the pattern below.

  

For the next figure $4$ , the number of new branches will be $81$ and foer the figure 5, the number of new branches will be $243$ . Therefore the complete table is,

x (number offigures)	y (number of new branches)
1	3
2	9
3	27
4	81
5	243

The relationship of number of figures and number of new branches is expressed in words as follows:

Words: For the each new figure, the number of new branches becomes three times the older

one.

Equation: From the pattern, the relationship between number of new branches and number oif figures is written in the form of equation as follows:

  $y\text{=}{\text{3}}^x$

From the table the ordered pairs are:

  $\left(1,3\right),\left(2,9\right),\left(3,27\right),\left(4,81\right),\left(5,243\right)$

The ordered pairs are plotted on the graph as follows: