Amadou bought a plant and planted it in a pot near a window in his house. The plant grew at a rate of 2.5 inches per month and its height at the time of purchase was 8 inches. Write an equation for H, commaH, in terms of t, commat, representing the height, in inches, of the plant tt months after Amadou bought the plant.

Answer 1

To express the height of the plant \( H \) in terms of the number of months \( t \) since Amadou bought it, we can use the following linear equation:

\[ H(t) = H_0 + r \cdot t \]

where:

• \( H_0 \) is the initial height of the plant at the time of purchase (8 inches),
• \( r \) is the growth rate of the plant (2.5 inches per month),
• \( t \) is the number of months since the plant was purchased.

Substituting the values for \( H_0 \) and \( r \):

\[ H(t) = 8 + 2.5t \]

So, the equation representing the height of the plant \( H \) in terms of the time \( t \) in months is:

\[ H(t) = 8 + 2.5t \]