When you receive Plant A, it is 4 cm tall and grows at a constant rate of 2 cm per month. When you receive Plant C, it is 8 cm tall and grows at a constant rate of 2 cm per month. Will the two plants ever be the same height? If so, when will that happen?

Question

How tall are both plants when you receive them?
Plant A is
cm tall, and Plant C is
cm tall.

Answer 1

When you receive the plants:

• Plant A is 4 cm tall.
• Plant C is 8 cm tall.

Both plants grow at a constant rate of 2 cm per month.

Let's denote the height of Plant A after \( t \) months as \( h_A(t) \) and the height of Plant C after \( t \) months as \( h_C(t) \).

• The height of Plant A after \( t \) months is: \[ h_A(t) = 4 + 2t \]

• The height of Plant C after \( t \) months is: \[ h_C(t) = 8 + 2t \]

Now, we want to determine if there will be a time \( t \) when the two heights are equal, i.e., when \( h_A(t) = h_C(t) \).

Setting the equations equal to each other: \[ 4 + 2t = 8 + 2t \]

Subtracting \( 2t \) from both sides results in: \[ 4 = 8 \]

This is a contradiction, which means that there is no value of \( t \) for which the heights of Plant A and Plant C will be the same.

Thus, the answer is that the two plants will never be the same height.

To summarize:

• Plant A is 4 cm tall when you receive it.
• Plant C is 8 cm tall when you receive it.