To determine which situation is represented by the table, we need to analyze the growth pattern of the plant based on the data provided. The table shows the height of the plant at specific weeks:
- At 2 weeks, height = 10 inches
- At 4 weeks, height = 15 inches
- At 6 weeks, height = 20 inches
- At 8 weeks, height = 25 inches
Now, let's find the growth rate:
-
From 2 weeks to 4 weeks: \( 15 - 10 = 5 \) inches over 2 weeks, giving a rate of \( \frac{5}{2} = 2.5 \) inches per week.
-
From 4 weeks to 6 weeks: \( 20 - 15 = 5 \) inches over 2 weeks, again \( \frac{5}{2} = 2.5 \) inches per week.
-
From 6 weeks to 8 weeks: \( 25 - 20 = 5 \) inches over 2 weeks, yet again \( \frac{5}{2} = 2.5 \) inches per week.
The consistent growth rate is determined to be 2.5 inches per week.
Next, let's find out the initial height (the height when Ms. Perry bought the plant). Since we know the rate of growth and the height at 2 weeks, we can work backward:
- At 2 weeks (10 inches), we can find the height at purchased time (0 weeks):
- If the plant grew at 2.5 inches per week, then in 2 weeks, it would have grown \( 2.5 \times 2 = 5 \) inches.
- So, the initial height would be \( 10 - 5 = 5 \) inches.
Based on this analysis, the conditions from the options are:
- A: Initial height = 10 inches, growth = 2.5 inches/week (not correct).
- B: Initial height = 5 inches, growth = 2.5 inches/week (correct).
- C: Initial height = 7.5 inches, growth = 1.5 inches/week (not correct).
- D: Initial height = 7.5 inches, growth = 5 inches/week (not correct).
Thus, the correct answer is:
B. When Ms. Perry bought the plant, its height was 5 inches. The plant grew at the rate of 2.5 inches per week.
1 answer