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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
Answer
To create the table, we start with the initial heights of each plant: 16 cm for Plant A and 24 cm for Plant B. We then calculate the height of each plant for each day by adding the growth amount for each day:
| Day | Plant A (cm) | Plant B (cm) |
|---|---|---|
| 1 | 16 | 24 |
| 2 | 20 | 27 |
| 3 | 24 | 30 |
| 4 | 28 | 33 |
| 5 | 32 | 36 |
| 6 | 36 | 39 |
| 7 | 40 | 42 |
Step 2
Write down two formulas – one for each plant
Answer
Let ( f(x) ) represent the height in centimeters of plant A, ( x ) days after John bought it. The growth of plant A is 4 cm per day.
[ f(x) = 16 + 4x ]
Let ( g(x) ) represent the height in centimeters of plant B, ( x ) days after John bought it. The growth of plant B is 3 cm per day.
[ g(x) = 24 + 3.5x ]
Where ( f(x) ) and ( g(x) ) give the heights of plant A and B respectively.
Step 3
Draw graphs to represent the heights of the two plants over the first four weeks
Answer
Using the formulas established, we can plot the graphs for plant A and plant B for up to 28 days (4 weeks). Each graph line represents the height of the respective plant over time. The x-axis will represent the days, and the y-axis will represent the heights in centimeters.
Step 4
From your diagram, write down the point of intersection of the two graphs
Answer
The point of intersection can be derived from the graphs, where the y-values for each function are equal. For this example, the point of intersection occurs at (16, 80), indicating that on the 16th day, both plants have the same height of 80 cm.
Step 5
Explain what the point of intersection means, with respect to the two plants
Answer
The point of intersection at (16, 80) means that on day 16, the heights of both plants are equal to 80 cm. The x-coordinate signifies the day, while the y-coordinate represents the height in centimeters for both plants.
Step 6
Step 7
Step 8
State one limitation of the model that might affect the point of intersection
Answer
One limitation of the model is that it assumes both plants grow at constant rates. This may not be realistic, as growth rates can vary due to environmental factors, which could impact the accuracy of the predicted point of intersection.