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 fast does each plant grow?
Plant A grows
cm per month and Plant C grows
cm per month.

Answer 1

To determine if Plant A and Plant C will ever be the same height, we can set up equations based on their heights over time.

Let:

• \( h_A(t) \) be the height of Plant A at time \( t \) months.
• \( h_C(t) \) be the height of Plant C at time \( t \) months.

Given:

• Plant A starts at 4 cm and grows at 2 cm per month: \[ h_A(t) = 4 + 2t \]

• Plant C starts at 8 cm and also grows at 2 cm per month: \[ h_C(t) = 8 + 2t \]

We need to determine if there is a time \( t \) when \( h_A(t) = h_C(t) \). This gives the equation: \[ 4 + 2t = 8 + 2t \]

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

This equation is not true, indicating that there will never be a time when the heights of the two plants are the same.

Growth Rates:

• Plant A grows 2 cm per month.
• Plant C grows 2 cm per month.

In conclusion, the two plants will never be the same height since they are growing at the same rate but started at different heights (4 cm for Plant A and 8 cm for Plant C).