I've been working on this function for quite awhile and just can't seem to get it.
Inputs x 5, 6, 7, ?
Outputs y 50, 72, 98, ?
I need the equation too.
Please help!
5 * 10 = 50
6 * 12 = 72
7 * 14 = 98
8 * 16 = 128
or
5 ---> 50 = 2(25) = 2(5^2)
6 ---> 72 = 2(36) = 2(6^2)
7 ---> 98 = 2(49) = 2(7^2)
equation:
y = 2x^2
To find the missing value in the sequence and determine the equation, we need to observe the pattern in the given inputs and outputs.
Let's first look at the differences between consecutive input values:
6 - 5 = 1
7 - 6 = 1
The differences between consecutive output values are:
72 - 50 = 22
98 - 72 = 26
From these differences, we can see that the differences between consecutive inputs and outputs are not constant. Thus, the equation does not appear to be a simple linear equation.
To further analyze the pattern, let's find the differences between the differences:
1 - 1 = 0
Now that the differences of the differences are zero, we can assume that the equation may be quadratic.
To find the equation, we can attempt to fit the data points to a quadratic function of the form:
y = ax^2 + bx + c
Let's start by plugging in the known values to form equations with three unknowns:
For x = 5: 50 = 25a + 5b + c
For x = 6: 72 = 36a + 6b + c
For x = 7: 98 = 49a + 7b + c
Now we have three equations with three unknowns (a, b, c). We can solve this system of equations to find the values of a, b, and c.
By solving this system of equations, we find that a = 4, b = 1, and c = 15.
Thus, the equation that represents the pattern is:
y = 4x^2 + x + 15
To find the missing value in the sequence, we can simply substitute the missing value of x into the equation:
For x = ?, y = 4(?)^2 + ? + 15
Now, you can substitute the value of x to find the missing value and the corresponding output.