Which type of function bet models the data in each table? Use differences
x y 12)
0 0
1 1.5
2 6
3 13.5
4 24
13)
x y
0 -5
1 -3
2 -1
3 1
4 3
14)
x y
0 1
1 1.2
2 1.44
3 1.728
4 2.0736
Can someone help me plz with these three??
Try mapping them out on graph paper. It should become evident.
ohh ok thanks!!
Sure! To determine the type of function that best models the data in each table using differences, you need to examine the differences between consecutive values of the y-coordinate for each table.
Let's start with table 12):
x y
0 0
1 1.5
2 6
3 13.5
4 24
To find the differences between consecutive y-values, we subtract the y-value at a specific x from the y-value at the next x. The differences for this table are:
1.5 - 0 = 1.5
6 - 1.5 = 4.5
13.5 - 6 = 7.5
24 - 13.5 = 10.5
Looking at the differences, we can see that they are not constant. This suggests that the function is not linear. Let's look at the differences of the differences:
4.5 - 1.5 = 3
7.5 - 4.5 = 3
10.5 - 7.5 = 3
The differences of the differences are constant. This indicates that the function is a quadratic function, specifically of the form y = ax^2 + bx + c.
Moving on to table 13):
x y
0 -5
1 -3
2 -1
3 1
4 3
The differences between the consecutive y-values are as follows:
-3 - (-5) = 2
-1 - (-3) = 2
1 - (-1) = 2
3 - 1 = 2
Both the differences and the differences of the differences are constant, indicating that the function is a linear function, specifically of the form y = mx + c (where m represents the slope and c represents the y-intercept).
Lastly, let's consider table 14):
x y
0 1
1 1.2
2 1.44
3 1.728
4 2.0736
The differences between the consecutive y-values are as follows:
1.2 - 1 = 0.2
1.44 - 1.2 = 0.24
1.728 - 1.44 = 0.288
2.0736 - 1.728 = 0.3456
The differences and differences of the differences are not constant. Therefore, the function does not appear to be linear or quadratic. To determine the type of function, we would need to analyze it further or gather more data points.
In summary:
- Table 12) is best modeled by a quadratic function (y = ax^2 + bx + c).
- Table 13) is best modeled by a linear function (y = mx + c).
- Table 14) does not clearly conform to any specific function based on the provided data.