Exercise 72 Page 179

In Part A we sketched Figures 0 and 4.

We can graph all figures together.

Now we can compare all figures by making a table of number of tiles in each figure.

Figure Number	Figure 0	Figure 1	Figure 2	Figure 3	Figure 4
Number of Tiles	5	11	17	23	29

We want to represent the pattern with a rule. Let's consider the form of the linear growth. y = mx + b For our rule, we will let x be the figure number and y be the number of tiles. In the formula, m represents the growth factor of the pattern and b represents the number of tiles in Figure 0. Let's remember the Figure 0 that we drew in Part A.

We can see that Figure 0 has 5 tiles. In Part A, we also found that each figure has 6 tiles more than the previous one. This means that the growth factor of the pattern is 6. Let's substitute these values to find the rule. y = mx + b ⇒ y = 6x + 5

We want to graph the number of tiles in each figure. Let's take a look at the table we made in Part B.

Figure Number	Figure 0	Figure 1	Figure 2	Figure 3	Figure 4
Number of Tiles	5	11	17	23	29

Now we will graph each (x,y) point on the same coordinate plane.

Let's take a look at the number of tiles in each figure.

Figure Number	Number of Tiles
0	5
1	5 + 6 = 11
2	11 + 6 = 17
3	17 + 6 = 23
4	23 + 6 = 29

We can see that each figure has 6 tiles more than the previous figure. This means that the growth factor of the pattern is 6.

We want to find how many tiles Figure 100 will have. We can use the rule that we wrote in Part C to do this. y = 6x + 5 Let's substitute 100 for x and simplify to get the number of tiles y.

Figure 100 will have 605 tiles.