Question

A plant has an initial height of 7 inches and grows at a constant rate of 3 inches each year. A second plant that also grows at a constant rate has an initial height of 2 inches and is 14 inches tall after 3 years. After how many years are the plants the same height?

The plants are the same height after year(s):

A. 10
B. 11
C. 12
D. 13
E. 15"

Answer 1

Using equations to represent the height growth of each plant, we find that the two plants will be the same height after 5 years. This result is not listed in the given options, indicating there may be an error in the multiple-choice options provided.

The correct answer is none of all.

Step-by-step explanation:

To find out after how many years the plants will be the same height, we can write equations for the growth of each plant and then solve for time when they have equal heights.

For the first plant, the height after t years can be described as: H1 = 7 + 3t (where 7 is the initial height in inches and 3 is the growth rate in inches per year).

For the second plant, we need to determine its growth rate. Since it grows from 2 inches to 14 inches in 3 years, it grows 12 inches in total over 3 years. Therefore, the growth rate is 12 inches / 3 years = 4 inches per year. Thus, the height after t years can be described as: H2 = 2 + 4t.

To find out when H1 equals H2, we set the two equations equal to each other:

7 + 3t = 2 + 4t

Solving for t, we subtract 3t from both sides and also subtract 2 from both sides to get:

5 = t

This means the plants will be the same height after 5 years, which is not one of the options provided in the problem, suggesting there might be a mistake in the multiple-choice options or in our understanding of the question.