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 \( t \) be the number of months after you receive the plants.
The height of Plant A after \( t \) months is: \[ \text{Height of Plant A} = 4 + 2t \]
The height of Plant C after \( t \) months is: \[ \text{Height of Plant C} = 8 + 2t \]
To find out if and when the two plants will be the same height, we can set the height equations equal to each other: \[ 4 + 2t = 8 + 2t \]
Subtract \( 2t \) from both sides: \[ 4 = 8 \]
This results in a contradiction, meaning that the two plants will never be the same height.
So to summarize:
- Plant A is 4 cm tall, and Plant C is 8 cm tall at the start.
- The two plants will never be the same height.