Answer:
y = x³ + 4
Step-by-step explanation:
Consider the differences between the values of y, that is
5 , 12 , 31 , 68 , 129
7 19 37 61 ← not constant
Now consider the differences of the first differences
7 , 19 , 37 , 61
12 18 24 ← not constant
Now consider the differences of the second differences
12 , 18 , 24
6 6 ← constant
Since the third differences are constant this indicates a cubic, that is
y = x³ + c ( where c is a constant )
Substitute the values of x into the equation
y = 1³ = 1 ← require to add 4 to obtain the required 5
y = 2³ = 8 ← require to add 4 to obtain the required 12
y = 3³ = 27 ← require to add 4 to obtain the required 31
y = 4³ = 64 ← require to add 4 to obtain the required 68
y = 5³ = 125 ← require to add 4 to obtain the required 129
Thus the equation is
y = x³ + 4
