Question

A scientist conducting an experiment creates a table to record the growth of two plants. The scientist uses the equations below to represent the growth of the plants, where w is the number of weeks of plant growth and h is the height of the plant in inches.
Plant 1:1.75 + 1/2w = h
Plant 2: 1.75 + 3/4w =h

Which describes the difference in the heights of the two plants in week 5?
Plant 1 is 1.25 inches taller than Plant 2.
Plant 2 is 1.25 inches taller than Plant 1.
Plant 1 is 1.75 inches taller than Plant 2.
Each plant is 1.75 inches tall.

Answer 1

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

$\textup{Plant 1: }\\\\1.75+\dfrac{1}{2}w=h~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\\textup{Plant 2: }1.75+\dfrac{3}{4}w=h~~~~~~~~~~~~~~~~~~~~~(ii)$

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

$\textup{Plant 1: }\\\\1.75+\dfrac{1}{2}w=h\\\\\\\Rightarrow h=1.75+\dfrac{1}{2}\times 5\\\\\\\Rightarrow h=1.75+2.5\\\\\Rightarrow h=4.25.$

and

$\textup{Plant 2: }\\\\1.75+\dfrac{3}{4}w=h\\\\\\\Rightarrow h=1.75+\dfrac{3}{4}\times 5\\\\\\\Rightarrow h=1.75+3.75\\\\\Rightarrow h=5.5.$

Therefore, the difference between the heights of the plants is

$5.5-4.25=1.25.$

Thus, plant 2 is 1.25 inches taller than plant 1.

Option (B) is correct.

Answer 2

Plant 1 in 5th week = 1.75 + 1/2 (5) = 1.75 + 2.5 = 4.25
Plant 2 in 5th week = 1.75 + 3/4 (5) = 1.75 + 3.75 = 5.50

So, Difference = 5.50 - 4.25 = 1.25

In short, Your Answer would be Option B

Hope this helps!