Answer: The correct option is (B) Plant 2 is 1.25 inches taller than Plant 1.
Step-by-step explanation: The equations representing the growth of the plants are given by
[tex]\textup{Plant 1: }\\\\1.75+\dfrac{1}{2}w=h~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\\textup{Plant 2: }1.75+\dfrac{3}{4}w=h~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
where, 'w' represents the number of weeks of plant growth and 'h' represents the height of the plant in inches.
We are to select the correct statement describes the difference in the heights of the two plants in week 5.
Substituting w = 5 in both the equations above, we have
[tex]\textup{Plant 1: }\\\\1.75+\dfrac{1}{2}w=h\\\\\\\Rightarrow h=1.75+\dfrac{1}{2}\times 5\\\\\\\Rightarrow h=1.75+2.5\\\\\Rightarrow h=4.25.[/tex]
and
[tex]\textup{Plant 2: }\\\\1.75+\dfrac{3}{4}w=h\\\\\\\Rightarrow h=1.75+\dfrac{3}{4}\times 5\\\\\\\Rightarrow h=1.75+3.75\\\\\Rightarrow h=5.5.[/tex]
Therefore, the difference between the heights of the plants is
[tex]5.5-4.25=1.25.[/tex]
Thus, plant 2 is 1.25 inches taller than plant 1.
Option (B) is correct.
