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:
[tex]h=2m+3[/tex]
Where h is the height and m is tshe number of months.
2. The constant rate of growth of the second plant is:
[tex]rate=\frac{29in-1in}{12months}=2.33inches/month[/tex]
3. Then, the expression is:
[tex]h=2.33m+1[/tex]
4. Equal both equations and solve for m:
[tex]2m+3=2.33m+1\\0.33m=2\\m=6.0[/tex]
5. Therefore, the plants have the same height after 6 months.
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,
[tex]h=3+2x[/tex]
Now, for second plant, the constant growth rate can be calculated as,
[tex]c=\dfrac{29-1}{12}\\c=\dfrac{7}{3}=2.33[/tex]
Now, the expression for height of the second plant can be written as,
[tex]h=1+2.33x[/tex]
If the height of two plants is same, then the value of x will be calculated as,
[tex]3+2x=1+2.33x\\2=0.33x\\x=6[/tex]
Therefore, after 6 months, the height of both the plants will be exactly same.
For more details, refer to the link:
https://brainly.com/question/13583528
