a Count the number of tiles each figure has to see how the pattern is changing.
B
b Recall that in this representation the x coordinate represents the figure number and the y coordinate represents the number of tiles
C
c Recall that in this representation x represent the number of the figure and y represents the number of tiles.
D
d Analyze the number of tiles each figure has to see how the pattern is changing.
A
aGrowth Factor: 5 tiles Number of tiles at Figure 0: 3 tiles.
B
bGrowth Factor: -2 tiles Number of tiles at Figure 0: 3 tiles.
C
cGrowth Factor: 3 tiles Number of tiles at Figure 0: -14 tiles.
D
dGrowth Factor: -5 tiles Number of tiles at Figure 0: 3 tiles.
Practice makes perfect
a We need to find the growth factor and the number of tiles for Figure 0 in the pattern shown below.
Let's start by counting the number of tiles each figure has to see how the pattern is changing and find what is being asked.
Figure 2 Figure 3 Figure 4
13 +5 → 18 +5 → 23
We can see that from figure to figure the number of tiles increases by 5. Therefore, Figure 1 should have 5 tiles less that Figure 2, meaning it will have 13-5=8 tiles. Figure 0 would have 5 tiles less than Figure 1, so Figure 0 would have 8-5= 3 tiles.
b We need to find the growth factor and the number of tiles for Figure 0 in the pattern representation given below.
In this representation the x coordinate represents the figure number and the y coordinate represents the number of tiles. From the graph, we can see that Figure 0 would have 3 tiles. Furthermore, the growth factor is -2, as the value is decreasing by 2 units at y as x increases by 1. This can be seen in the graph below.
c We need to find the growth factor and the number of tiles for Figure 0 in the pattern representation given below.
y= 3x-14
In this representation, x represents the number of the figure and y represents the number of tiles. Therefore, to find the number of tiles at Figure 0 we just need to evaluate the expression at x=0.
Hence, Figure 0 would have -14 tiles. To find the growth factor, notice that the coefficient of x is 3. Each time the figure number rises by 1 the number of tiles will rise by 3.
d We need to find the growth factor and the number of tiles for Figure 0 in the pattern representation given below.
x
-3
-2
-1
0
1
2
3
y
18
13
8
3
-2
-7
-12
Let's start by analyzing the number of tiles each figure has to see how the pattern is changing and find what is required.
x. -3 -2 -1 1 2
y. 18 -5 → 13 -5 → 8 -5 → 3 -5 → -2 -5 → -7
We can see that the pattern has 3 tiles at Figure 0. We also see that the number of tiles is decreasing from figure to figure by 5.
