Question

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?

Answer 1

Answer: 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:

$h=2m+3$

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

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

$rate=\frac{29in-1in}{12months}=2.33inches/month$

3. Then, the expression is:

$h=2.33m+1$

4. Equal both equations and solve for m:

$2m+3=2.33m+1\\0.33m=2\\m=6.0$

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