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\begin{tabular}{|c|c|}
\hline
Weeks & Height (in) \\
\hline
2 & 7.3 \\
\hline
3 & 8.7 \\
\hline
4 & 10.1 \\
\hline
\end{tabular}

Assume Plant B received sunlight, and its rate of change was 1.6 inches per week instead of 1.4 inches per week. Would it be taller at 6 weeks?

A. No. It will be shorter.
B. No. It will be the same height.
C. Yes. It will be 0.3 inches taller.
D. Yes. It will be 4.5 inches taller.


Sagot :

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.
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