Create a non linear equation for this table
x 1 2 3
y 3 12 27
One possible non-linear equation for this table is:
y = x^3
To create a non-linear equation for the given table, we need to find a pattern or relationship between the x and y values.
Looking at the x values, we can see that they are increasing by 1 each time: 1, 2, 3.
Looking at the y values, we can see that they are increasing at a faster rate: 3, 12, 27.
To determine the equation, let's first find the difference in y values: 12 - 3 = 9 and 27 - 12 = 15.
Now, let's find the difference in differences by subtracting the second differences from the first differences: 15 - 9 = 6.
Since the second differences are constant, we can conclude that the equation is quadratic. Therefore, we can infer that the equation is of the form y = ax^2 + bx + c.
Now, let's substitute the x and y values from the table into our equation to find the values of a, b, and c.
When x = 1, y = 3:
3 = a(1)^2 + b(1) + c
3 = a + b + c ...........(Equation 1)
When x = 2, y = 12:
12 = a(2)^2 + b(2) + c
12 = 4a + 2b + c ...........(Equation 2)
When x = 3, y = 27:
27 = a(3)^2 + b(3) + c
27 = 9a + 3b + c ...........(Equation 3)
Now, we have a system of three equations with three variables (a, b, and c) that we can solve simultaneously.
By solving this system of equations, we can find the values of a, b, and c, which will give us the non-linear equation for the table.
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 quadratic equation.
Let's assume the equation has the form:
y = ax^2 + bx + c
To find the coefficients a, b, and c, 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)^2 + b(1) + c
2. 12 = a(2)^2 + b(2) + c
3. 27 = a(3)^2 + b(3) + c
Simplifying these equations, we have:
1. a + b + c = 3
2. 4a + 2b + c = 12
3. 9a + 3b + c = 27
Solving this system of equations will give us the values of a, b, and c, and thus the non-linear equation that fits the table.
But that doesn't make sense because if you put 2 in place of x, you get 8 not 12. Try again!
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.