what is the rule of the input output table input 2 output 11 input 3 output 15 input 5 output 18 input 8 output? what is the rule?
2 --> 11
3 --> 15
5 --> 18
8 --> ??
slopes are different, so , not linear
assume it is quadratic
y = ax^2 + bx + c
11 = 4a+2b+c
15= 9a+3a+c
18 = 25a+5b+c
#2 - #1 ---> 5a + b = 4
#3 - #2 ---> 16a + 2b = 3
16a + 2b = 3
10a + 2b = 8
subtract
6a = -5
a = -5/6
then 5(-5/6) + b = 4
-25 + 6b = 24
6b = 49
b = 49/6
in 4a+2b+c=11
4(-5/6) + 2(49/6) + c = 11
-20 + 98 + 6c = 66
6c = -12
c = -2
y = (-5/6)x + (49/6)x-2
so if input = x = 8
y = output = (5/6)(8) + (49/6)(8) - 2
= 70
check:
if input is 2, output = (-5/6)(2) + (49/6)(2) - 2 = 11
if input is 3, out put = (-5/6)(9) + (49/6)(3) - 2 = 15
if input is 5, out put is (-5/6)(25) + (49/6)(5) - 2 = 18
All is good !
eqution is y=2exponet(x)+2 input value if y =34
To find the rule of the input-output table given, we need to analyze the pattern between the inputs and outputs. Let's look at the data provided:
Input Output
2 11
3 15
5 18
8 ?
To start, let's examine the difference between the inputs (2, 3, 5, 8). We can see that the sequence is not increasing by a consistent amount. The differences are 1, 2, and 3, respectively.
Now, let's examine the differences between the outputs (11, 15, 18). We can see that the sequence is not increasing by a consistent amount either. The differences are 4 and 3, respectively.
Since neither the input differences nor the output differences follow a consistent pattern, we can deduce that this table might not have a simple rule. However, we can still make an educated guess based on the available data.
Considering the inputs, we can observe that increasing the input value by 1 does not always result in a consistent increase in the output value. For example, when the input changes from 2 to 3, there is an increase in the output value of 4 (from 11 to 15). On the other hand, when the input changes from 3 to 5, there is only an increase of 3 in the output value (from 15 to 18). Therefore, there doesn't seem to be a linear relationship between the inputs and the outputs.
To find a possible rule for this table, we can try fitting a curve or using a non-linear function. However, without more data points, it is challenging to find a definitive rule. Therefore, we can only make an educated guess, but there is no clear rule evident from the given information.
In summary, based on the limited data provided, it seems that the given input-output table may not have a simple mathematical rule or pattern that can be easily determined.