Question

Create a non linear equation for this table
x 1 2 3
y 3 12 27

Answer 1

But that doesn't make sense because if you put 2 in place of x, you get 8 not 12. Try again!

Answer 2

One possible non-linear equation for this table is:

y = x^3

Answer 3

Apologies for the mistake. Let's try again.

To create a non-linear equation for the given table, we can observe the pattern between the values of x and y.

By looking at the values, we can see that the relationship between x and y is not a simple linear one, since the differences between successive y-values are not constant.

To find the non-linear equation for the table, we can try to fit the data points using a polynomial equation. Since the y-values seem to increase rapidly, we will consider using a cubic equation.

Let's assume the equation has the form:

y = ax^3 + bx^2 + cx + d

To find the coefficients a, b, c, and d, we can substitute the x and y values from the table into the equation to create a system of three equations:

1. 3 = a(1)^3 + b(1)^2 + c(1) + d
2. 12 = a(2)^3 + b(2)^2 + c(2) + d
3. 27 = a(3)^3 + b(3)^2 + c(3) + d

Simplifying these equations, we have:

1. a + b + c + d = 3
2. 8a + 4b + 2c + d = 12
3. 27a + 9b + 3c + d = 27

Solving this system of equations will give us the values of a, b, c, and d, and thus the non-linear equation that fits the table.