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John is given two sunflower plants - Leaving Cert Mathematics - Question 8 - 2014
Question 8
John is given two sunflower plants. One plant is 16 cm high and the other is 24 cm high. John measures the height of each plant at the same time every day for a week... show full transcript
Worked Solution & Example Answer:John is given two sunflower plants - Leaving Cert Mathematics - Question 8 - 2014
Step 1
Draw up a table showing the heights of the two plants each day for the week, starting on the day that John got them.
Answer
To create the table, we note the initial heights and the daily growth rates:
| Day | Height of Plant A (cm) | Height of Plant B (cm) |
|---|---|---|
| 0 | 16 | 24 |
| 1 | 20 | 27.5 |
| 2 | 24 | 31 |
| 3 | 28 | 34.5 |
| 4 | 32 | 38 |
| 5 | 36 | 41.5 |
| 6 | 40 | 45 |
| 7 | 44 | 48.5 |
Step 2
Write down two formulas – one for each plant – to represent the heights of the two plants on any given day. State clearly the meaning of any letters used in your formulas.
Answer
Let:
- represent the height of Plant A in centimeters after days.
- represent the height of Plant B in centimeters after days.
The formulas are:
- For Plant A:
- For Plant B:
Where is the number of days since John got the plants.
Step 3
John assumes that the plants will continue to grow at the same rates. Draw graphs to represent the heights of the two plants over the first four weeks.
Answer
The graphs can be plotted based on the formulas derived in part (b). You should plot and over the range from 0 to 28 days (4 weeks). The x-axis will represent the days, and the y-axis will represent the height in centimeters. The graphs will show linear trends for both plants.
Step 4
Step 5
(ii) Explain what the point of intersection means, with respect to the two plants.
Answer
The point of intersection (16, 80) indicates that on day 16 both plants will be at a height of 80 cm. This means that at this point in time, Plant A (originally shorter) will have caught up in height with Plant B.
Step 6
Step 7
The point of intersection can be found either by reading the graph or by using algebra. State one advantage of finding it using algebra.
Answer
By using algebra, we can find the point of intersection exactly without any errors. Reading from a graph can sometimes lead to approximations, which may not be accurate.
Step 8
John’s model for the growth of the plants might not be correct. State one limitation of the model that might affect the point of intersection and its interpretation.
Answer
This model assumes that both plants grow at constant rates throughout the entire duration. In reality, plant growth can vary due to factors such as changes in sunlight, water availability, and other environmental conditions.