Question

Heeeelllpppp !

Activity 2

Figures 1, 2, 3, and 4 are shown. The x-value is the number of the pattern and the y-value is the number of green triangles.

Enter the four data points, graph the data, and choose a function f(x) whose graph will pass through the points.

If this pattern were to continue, how many triangles would be the area of the 7th figure?

Answer 1

first start by creating a table

x y

1 1

2 3

3 9

4 27
.

.
.
.
.
7 ?


how i solved it was by looking at the differences between the iterations, and if they're not the same, you look at the differences between the differences until they are all similar. This is how i found the geometric pattern between the two. It is not arithmetic so you have to use a little logic


the function I came up with is:
\[y = 3^{x-1}\]

where y is the number of green triangles and x is the iteration number

Answer 2

so to find the number of green triangles of the 7th figure, substitute x = 7 and solve for y

Answer 3

omg thank you! I have 2 more do you think you could help? They are like this? I'll ask them on a separate thing, so I can give you a metal again.