For the first table:
The relationship represented by the table is an exponential relationship. This can be determined by observing that as the value of X increases by 1, the value of Y increases by a constant factor of 1.5. In an exponential relationship, the dependent variable (Y) changes by a constant ratio or factor as the independent variable (X) changes.
By Rule:
The correct rule that represents the relationship in the first table is option 3: Y = 5(1.5)^x. This rule accurately shows that the value of Y is determined by multiplying 5 with 1.5 raised to the power of X.
For the second table:
The relationship represented by the table is a linear relationship. This can be determined by observing that as the value of X increases by 1, the value of Y increases by a constant amount of 18. In a linear relationship, the dependent variable (Y) changes by a constant amount as the independent variable (X) changes.
By Rule:
The correct rule that represents the relationship in the second table is option 2: Y = 18x - 6. This rule accurately shows that the value of Y is determined by multiplying 18 with X and then subtracting 6.