what is the rule if the input is 1 and output is 9 and input is 2 and output is 12 and the input is 3 and output 16
1 ---> 9
2 ---> 12
3 ---> 16
hard to tell, it is not linear,
I don't know what level this is,
let's assume it is a quadratic
I did some quick calculations and got
y = (1/2)x^2 + (3/2)x + 7
or
y = (x^2 + 3x + 14)/2
works for your 3 values
To find the pattern or rule between the input and the output, we can analyze the given data and observe the changes.
Let's look at the differences between the inputs and the corresponding outputs:
- The difference between the input 1 and the output 9 is 8.
- The difference between the input 2 and the output 12 is 10.
- The difference between the input 3 and the output 16 is 13.
From these differences, we can see that the values are increasing by 2 each time. So, we can conclude that the rule or pattern for this input-output relationship is:
Output = (Input^2) + (Input * 2)
Therefore, if we continue this pattern:
- Input 4 will give Output = (4^2) + (4 * 2) = 16 + 8 = 24.
To determine the rule or pattern in the given inputs and outputs, we need to observe the relationship between the numbers. Let's look for any patterns or trends:
When the input is 1, the output is 9.
When the input is 2, the output is 12.
When the input is 3, the output is 16.
Let's subtract the input number by 1 and multiply it by a specific value and then add a constant value to obtain the output.
Let's do some calculations to verify if this pattern holds true for all the given inputs:
For input 1:
(1 - 1) * X + C = 9
0 * X + C = 9
C = 9
For input 2:
(2 - 1) * X + C = 12
1 * X + 9 = 12
X + 9 = 12
X = 3
So, the rule is:
Multiply the input number by 3 and add 9 to get the output number.
Therefore, when the input is any number N, the output can be calculated using the rule: 3N + 9.