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Question 1

Megan and Suzanne each have a plant. They track the growth of their plants for four weeks. Whose plant grew at a faster rate, and what was the rate?

Suzanne's Plant:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Week} & \text{Plant Height (in)} \\
\hline
1 & 4.5 \\
\hline
2 & 7 \\
\hline
3 & 9.5 \\
\hline
4 & 12 \\
\hline
\end{array}
\][/tex]

A. Suzanne's at 2 inches per week
B. Suzanne's at 1.5 inches per week
C. Megan's at 3 inches per week
D. Megan's at 2.5 inches per week


Sagot :

To accurately determine which plant grew at a faster rate, we need to calculate the growth rate for both Megan's and Suzanne's plants and then compare them.

### Megan's Plant Growth Rate

Megan measured her plant's height over four weeks as follows:

[tex]\[ \begin{array}{|c|c|} \hline \text{Week} & \text{Plant Height (in)} \\ \hline 1 & 4.5 \\ \hline 2 & 7 \\ \hline 3 & 9.5 \\ \hline 4 & 12 \\ \hline \end{array} \][/tex]

To find the weekly growth rate of Megan's plant, we can use the following formula for the average rate of change over the given period:

[tex]\[ \text{Growth Rate} = \frac{\text{Final Height} - \text{Initial Height}}{\text{Number of Weeks} - 1} \][/tex]

Plugging in Megan's data:

[tex]\[ \text{Growth Rate} = \frac{12 - 4.5}{4 - 1} = \frac{7.5}{3} = 2.5 \ \text{inches per week} \][/tex]

### Suzanne's Plant Growth Rate

Suzanne's plant grows at a constant rate. We are given that the growth rate for Suzanne's plant is:

[tex]\[ 2 \ \text{inches per week} \][/tex]

### Comparison and Conclusion

We now compare the two growth rates:

- Megan's Plant: 2.5 inches per week
- Suzanne's Plant: 2 inches per week

From the comparison, it is clear that Megan's plant grew at a faster rate of 2.5 inches per week.

Thus, the correct answer is:

d) Megan's at 2.5 inches per week
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