Let's analyze the situation step by step to determine if Plant B would be taller at 6 weeks.
### Given Data
- Plant A's heights at different times:
- 2 weeks: 7.3 inches
- 3 weeks: 8.7 inches
- 4 weeks: 10.1 inches
- Growth rate of Plant A: 1.4 inches per week
### Finding Initial Height of Plant A
We need to find the initial height of Plant A at 0 weeks. To do this, we can use the given data point for 2 weeks (7.3 inches).
Since height = initial height + (growth rate) * (number of weeks), we can set up the equation:
[tex]\[ 7.3 = \text{initial height} + 1.4 \times 2 \][/tex]
Solving for the initial height:
[tex]\[ \text{initial height} = 7.3 - (1.4 \times 2) \][/tex]
[tex]\[ \text{initial height} = 7.3 - 2.8 \][/tex]
[tex]\[ \text{initial height} = 4.5 \text{ inches} \][/tex]
### Height of Plant A at 6 Weeks
Using the initial height and the growth rate of 1.4 inches per week, we can calculate the height of Plant A at 6 weeks:
[tex]\[ \text{Height at 6 weeks} = 4.5 + (1.4 \times 6) \][/tex]
[tex]\[ \text{Height at 6 weeks} = 4.5 + 8.4 \][/tex]
[tex]\[ \text{Height at 6 weeks} = 12.9 \text{ inches} \][/tex]
### Height of Plant B at 6 Weeks
Plant B has a growth rate of 1.6 inches per week. Assuming the same initial height as Plant A, we can calculate the height of Plant B at 6 weeks:
[tex]\[ \text{Height at 6 weeks} = 4.5 + (1.6 \times 6) \][/tex]
[tex]\[ \text{Height at 6 weeks} = 4.5 + 9.6 \][/tex]
[tex]\[ \text{Height at 6 weeks} = 14.1 \text{ inches} \][/tex]
### Difference in Height at 6 Weeks
The height difference between Plant B and Plant A at 6 weeks is:
[tex]\[ \text{Height difference} = 14.1 - 12.9 \][/tex]
[tex]\[ \text{Height difference} = 1.2 \text{ inches} \][/tex]
### Conclusion
Since Plant B would be taller at 6 weeks by 1.2 inches, the correct answer is:
Yes. It will be 1.2 inches taller.
However, as per the options provided:
- No. It will be shorter.
- No. It will be the same height.
- Yes. It will be 0.3 inches taller.
- Yes. It will be 4.5 inches taller.
It seems like there might be a misprint or error in the provided choices because the closest correct inference is not exactly listed. Based on all calculations given and the answers provided within our steps, Plant B is indeed taller by 1.2 inches.
