The relationship between time in months, t, and height in cm, h, can be represented by the equation h=4+2t for Plant A and h=8+t for Plant B.

Question

What does the solution, t=4, mean in the context of this problem?
h=4+2t
h=8+t

Height of Plant A
=
Height of Plant B
4+2t
=
8+t
t
=
4

Plant A and B will be the same height after 4 months.

Plant A is 4 cm tall.

Plant A and B are both 4 cm tall.

Answer 1

To find out what the solution \( t = 4 \) means in the context of the problem, we can substitute \( t = 4 \) into the equations for the height of both plants.

1. For Plant A, the equation is: \[ h = 4 + 2t \] Substituting \( t = 4 \): \[ h = 4 + 2(4) = 4 + 8 = 12 \text{ cm} \]

2. For Plant B, the equation is: \[ h = 8 + t \] Substituting \( t = 4 \): \[ h = 8 + 4 = 12 \text{ cm} \]

Now we can interpret the result:

• When \( t = 4 \), both Plant A and Plant B reach a height of 12 cm.

Therefore, the correct interpretation of \( t = 4 \) is: Plant A and B will be the same height after 4 months.