Answer: 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
