Item 19 a plant has an initial height of 3 inches and grows at a constant rate of 2 inches each month. a second plant that also grows at a constant rate has an initial height of 1 inch and is 29 inches tall after 1 year. after how many months are the plants the same height?

The plants grow at a constant rate. After 6 months, the height of both the plants will be exactly the same.

Given information:

A plant has an initial height of 3 inches and grows at a constant rate of 2 inches each month.

The second plant that also grows at a constant rate has an initial height of 1 inch and is 29 inches tall after 1 year or 12 months.

Let x presents the number of months and c represents the rate of growth of the second plant. h be the height of plants after x months.

The expression for height of the first plant can be written as,

Now, for second plant, the constant growth rate can be calculated as,

Now, the expression for height of the second plant can be written as,

If the height of two plants is same, then the value of x will be calculated as,

Therefore, after 6 months, the height of both the plants will be exactly same.

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6 months

Step-by-step explanation:

1. If the first plant has an initial height of 3 inches and grows at a constant rate of 2 inches each month, you can write the following expression:

Where h is the height and m is tshe number of months.

2. The constant rate of growth of the second plant is:

3. Then, the expression is:

4. Equal both equations and solve for m:

5. Therefore, the plants have the same height after 6 months.

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step-by-step explanation: