Which function has greater rate of change?
Table 1
x
2
5
6
9
y
5
11
13
19
Table 2
x
2
5
6
9
y
4
13
16
25
Table 1
Table 2
Both the tables have the same rate of change
None of the choices
To find the rate of change for each table, we can calculate the difference in y-values for each corresponding pair of x-values.
For Table 1, the rate of change is as follows:
(11 - 5) = 6 for x = 5 to x = 2
(13 - 11) = 2 for x = 6 to x = 5
(19 - 13) = 6 for x = 9 to x = 6
For Table 2, the rate of change is as follows:
(13 - 4) = 9 for x = 5 to x = 2
(16 - 13) = 3 for x = 6 to x = 5
(25 - 16) = 9 for x = 9 to x = 6
Therefore, the rate of change for Table 2 is greater than the rate of change for Table 1.
To determine which function has a greater rate of change, we need to compare the differences in the y-values for the same differences in the x-values in both tables.
For Table 1, the differences in y-values are:
5 - 2 = 3
11 - 5 = 6
13 - 6 = 7
19 - 13 = 6
For Table 2, the differences in y-values are:
4 - 2 = 2
13 - 5 = 8
16 - 6 = 10
25 - 9 = 16
Comparing these differences, we see that the rate of change in Table 2 is greater than the rate of change in Table 1. Therefore, the function described by Table 2 has a greater rate of change.