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?

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

1 answer

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.