he 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

We just found that t, the time in months, is 4. That means the two plants are the same height after 4 months. When we graphed the equations, we saw that at 4 months, both plants had a height of 12 cm. Let’s confirm that with the equations. Start by substituting 4 for t in the equation for Plant A.
Height of Plant A: h=4+2t
h=4+2(
)

Answer 1

To find the height of Plant A at \( t = 4 \) months, we can substitute 4 into the equation \( h = 4 + 2t \).

Starting with the equation:

\[ h = 4 + 2t \]

Now, substituting \( t = 4 \):

\[ h = 4 + 2(4) \]

Calculating this step-by-step:

1. Compute \( 2 \times 4 = 8 \).
2. Now add that to 4: \( 4 + 8 = 12 \).

So, the height of Plant A after 4 months is:

\[ h = 12 \text{ cm} \]

Now let's check Plant B using the same value of \( t = 4 \) in its equation \( h = 8 + t \).

\[ h = 8 + t \]

Substituting \( t = 4 \):

\[ h = 8 + 4 \]

Calculating this:

\[ h = 12 \text{ cm} \]

Thus, both Plant A and Plant B have the same height of 12 cm after 4 months.