Which table has the greatest rate of change over the interval from 1 to 4? (1 point)
1
h(a) o
4
g
5
10
f (2) 0 2 5 15
](a) 22
23
3
26
4
30
+ G.
28
Based on the information given, it is not possible to determine which table has the greatest rate of change over the interval from 1 to 4. There is no information provided about the rate of change for any of the tables.
To find the table with the greatest rate of change over the interval from 1 to 4, we need to calculate the rate of change for each table over that interval.
Using the formula for rate of change (also known as slope), we can calculate the slope of each table over the given interval.
Table h(a):
Slope = (h(4) - h(1)) / (4 - 1)
= (10 - 4) / (3)
= 6 / 3
= 2
Table g:
Slope = (28 - 23) / (4 - 1)
= (5) / (3)
= 5/3
Table f:
Slope = (f(4) - f(1)) / (4 - 1)
= (30 - 15) / (3)
= 15 / 3
= 5
Comparing the slopes of the three tables, we can see that the table with the greatest rate of change over the interval from 1 to 4 is Table h(a), with a slope of 2.
To determine which table has the greatest rate of change over the interval from 1 to 4, we need to calculate the rate of change for each table.
The rate of change represents how a dependent variable (in this case, the y-values) changes with respect to an independent variable (in this case, the x-values). It is calculated by finding the difference in y-values divided by the difference in x-values.
Let's calculate the rate of change for each table:
Table 1 (h):
Rate of change = (h(4) - h(1)) / (4 - 1) = (10 - 5) / 3 = 5/3 ≈ 1.67
Table 2 (g):
Rate of change = (g(4) - g(1)) / (4 - 1) = (23 - 22) / 3 = 1/3 ≈ 0.33
Table 3 (f):
Rate of change = (f(4) - f(1)) / (4 - 1) = (30 - 15) / 3 = 15/3 = 5
Table 4 (not provided):
Since no information is given for table "G," we cannot calculate the rate of change for this table.
Comparing the calculated rates of change, we can see that Table 3 (f) has the greatest rate of change over the interval from 1 to 4. Its rate of change is 5, which is higher than the rates of change for the other tables.