The second table could represent relationship B.
Step-by-step explanation:
Step 1:
The tables give a relationship between the growth of a plant and the number of weeks it took.
To determine the rate of each table, we determine the growth of the plant in a single week.
The growth rate in a week = [tex]\frac{Difference in height}{time taken}[/tex].
Step 2:
For the given graph, the points are (4, 3) and (8, 6).
The growth rate in a week = [tex]\frac{Difference in height}{time taken} = \frac{6-3}{8-4}=\frac{3}{4} = 0.75.[/tex]
So the growth rate for relationship A is 0.75.
Step 3:
Now we calculate the growth rates of the given tables.
Table 1's growth rate in a week = [tex]\frac{Difference in height}{time taken} = \frac{3-1.2}{5-2}=\frac{1.8}{3} = 0.6.[/tex]
Table 2's growth rate in a week = [tex]\frac{Difference in height}{time taken} = \frac{4-1.6}{5-2}=\frac{2.4}{3} = 0.8.[/tex]
Table 3's growth rate in a week = [tex]\frac{Difference in height}{time taken} = \frac{2-1.5}{4-3}=\frac{0.5}{1} =0.5.[/tex]
Table 4's growth rate in a week = [tex]\frac{Difference in height}{time taken} = \frac{3.5-1.4}{5-2}=\frac{2.1}{3} = 0.7.[/tex]
Since relationship B has a greater rate than A, Table 2 is relationship B.
