Type an equation for the following pattern x: 1 | 2 | 3 | 4 | 5 y: 6 | 18 | 54 | 162 |486

y = 6(3)ˣ⁻¹

Explanation:

x    |    y

1    |    6        

2    |    18      

3    |    54    

4    |    162    

5    |    486  

The x-coordinates increase by one.  Now look at the y-coordinates.  If you factor out a 6, you can see a pattern.  

x    |    y

1    |    6        = 6(1)

2    |    18      = 6(3)

3    |    54     = 6(9)

4    |    162    =6(27)

5    |    486   = 6(81)

What do 1, 3, 9, 27, and 81 have in common? Three is their only factor.

x    |    y

1    |    6        = 6(1)   = 6(3)⁰

2    |    18      = 6(3)   = 6(3)¹

3    |    54     = 6(9)   = 6(3)²

4    |    162    =6(27)   = 6(3)³

5    |    486   = 6(81)   = 6(3)⁴

How does the exponent compare to the x-value? It is x - 1

Now we have enough information to write the equation: y = 6(3)ˣ⁻¹