To determine if Simon's claim is correct, we need to analyze the growth patterns of both Plant A and Plant B. Let's break down the information step-by-step.
### Step 1: Determine the growth rate (slope) and initial value (intercept) for Plant A.
For Plant A, we have the following data points:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Weeks} & \text{Height (in)} \\
\hline
2 & 7.3 \\
\hline
3 & 8.7 \\
\hline
4 & 10.1 \\
\hline
\end{array}
\][/tex]
Using linear regression, we find the line of best fit for these data points. The equation of a line is given by [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
For Plant A, the slope ([tex]\( m \)[/tex]) is approximately [tex]\( 1.4 \)[/tex], and the y-intercept ([tex]\( b \)[/tex]) is approximately [tex]\( 4.5 \)[/tex].
### Step 2: Calculate the height of Plant A at 6 weeks.
Using the linear equation [tex]\( y = 1.4x + 4.5 \)[/tex], we substitute [tex]\( x = 6 \)[/tex] to find the height of Plant A at 6 weeks:
[tex]\[
\text{Height of Plant A at 6 weeks} = 1.4 \times 6 + 4.5 = 8.4 + 4.5 = 12.9 \text{ inches}
\][/tex]
### Step 3: Given the initial value and growth rate for Plant B.
For Plant B, we know:
- Initial value (intercept): [tex]\( 0.9 \)[/tex] inches
- Growth rate (slope): [tex]\(1.4 \)[/tex] inches/week
### Step 4: Calculate the height of Plant B at 6 weeks.
Using the linear equation [tex]\( y = 1.4x + 0.9 \)[/tex] for Plant B, substitute [tex]\( x = 6 \)[/tex]:
[tex]\[
\text{Height of Plant B at 6 weeks} = 1.4 \times 6 + 0.9 = 8.4 + 0.9 = 9.3 \text{ inches}
\][/tex]
### Step 5: Compare the heights of Plant A and Plant B at 6 weeks.
- Height of Plant A at 6 weeks: [tex]\( 12.9 \)[/tex] inches
- Height of Plant B at 6 weeks: [tex]\( 9.3 \)[/tex] inches
Plant A is taller than Plant B at 6 weeks.
### Step 6: Conclusion based on the analysis.
Simon's claim that "Plant B will be taller than Plant A in 6 weeks because it has the greater initial value" is incorrect.
The correct interpretation is:
- Though Plant B has a higher initial value, the greater rate of change (slope) of Plant A results in Plant A being taller at 6 weeks.
Therefore, the accurate response from the given options is:
No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.
