To determine the pattern for the points that represent the total amount of food and water Julian gives Banjo over one week, we can examine the data provided.
Each day, Julian gives:
- Water: 3 liters
- Food: 500 grams
Over one week (which is 7 days), the amount of water and food given to Banjo will accumulate.
For the x-coordinate:
Each day represents a day, so the x-coordinate will start at 3 (for the first day) and increase by 1 for each subsequent day. Thus:
- Day 1 (x=1): (3, 500)
- Day 2 (x=2):
- Day 3 (x=3):
- Day 4 (x=4):
- Day 5 (x=5):
- Day 6 (x=6):
- Day 7 (x=7):
The x-coordinate increases by 1 each day.
For the y-coordinate:
Each day, Banjo receives 3 liters of water and 500 grams of food. Over 7 days, we can calculate the total as follows:
- Water for 7 days = \(3 \times 7 = 21\) liters
- Food for 7 days = \(500 \times 7 = 3500\) grams
The total amount of food and water would be represented by:
- Total water (in grams) = \(21 \text{ liters} = 21 \times 1000 = 21000 \text{ grams}\) (if combining food and water in grams)
- Total food = 3500 grams
Converted, the total (in grams) becomes \(21000 + 3500 = 24500\) grams.
However, the points themselves will evolve as follows from the first day:
- For Day 2 (x=2): y-coordinate = \(3 \times 2 + 500 \times 2 = 6 + 1000 = 1006\)
- For Day 3 (x=3): y-coordinate = \(3 \times 3 + 500 \times 3 = 9 + 1500 = 1509\)
Continuing this for the other days, the y-coordinate also increases consistently:
- Each day contributes an additional 3 liters + 500 grams to the total from the previous day.
So:
- The y-coordinate increases by \(3 + 500 = 503\) grams each day.
Final Pattern Description:
- Each day, the x-coordinate increases by 1.
- Each day, the y-coordinate increases by 503 grams.
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