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

Are the two plants the same height when you receive them?

Yes

No

Answer 1

To determine if the two plants will ever be the same height, we can set up equations for their heights over time.

Let \(t\) represent the number of months after you receive the plants.

1. Height of Plant A after \(t\) months: \[ \text{Height of Plant A} = 4, \text{cm} + 2, \text{cm/month} \times t = 4 + 2t \]

2. Height of Plant C after \(t\) months: \[ \text{Height of Plant C} = 8, \text{cm} + 2, \text{cm/month} \times t = 8 + 2t \]

Next, we can set the heights of the plants equal to each other to find out when they will be the same height: \[ 4 + 2t = 8 + 2t \]

Subtract \(2t\) from both sides: \[ 4 = 8 \]

This statement is false, which means that the two heights will never be equal. Therefore, the two plants will not be the same height at any time in the future.

To answer your sub-questions:

1. Will the two plants ever be the same height? No.
2. Are the two plants the same height when you receive them? No (Plant A is 4 cm and Plant C is 8 cm).