Ankit is measuring how fast bacteria grow in a dish by measuring the area that the bacteria cover. On day 1, the bacteria cover `0.35cm^(2)`. On day 2, they cover `0.70cm^(2)`. On day 3, they cover `1.40cm^(2)`. What is the best prediction for the area covered on day 4?

Options

A. `1.50 cm^(2)`
B. `3 cm^(2)`
C. `2.80 cm^(2)`
D. `2.90 cm^(2)`

Answer

To predict the area covered by the bacteria on day 4, we can analyze the data provided for the first three days:

1. **Data Collection**:
- Day 1: Area covered = 0.35 cm²
- Day 2: Area covered = 0.70 cm²
- Day 3: Area covered = 1.40 cm²

2. **Identifying the Pattern**:
- From Day 1 to Day 2:
- Increase = 0.70 cm² - 0.35 cm² = 0.35 cm²
- From Day 2 to Day 3:
- Increase = 1.40 cm² - 0.70 cm² = 0.70 cm²

3. **Calculating the Growth Rate**:
- The increase from Day 1 to Day 2 is 0.35 cm².
- The increase from Day 2 to Day 3 is 0.70 cm², which is double the increase from Day 1 to Day 2.

4. **Extrapolating to Day 4**:
- If the pattern continues, we can assume that the increase from Day 3 to Day 4 will also double the previous increase.
- Therefore, the increase from Day 3 to Day 4 would be:
- Increase = 0.70 cm² × 2 = 1.40 cm²

5. **Calculating the Area for Day 4**:
- Area covered on Day 4 = Area on Day 3 + Increase
- Area covered on Day 4 = 1.40 cm² + 1.40 cm² = 2.80 cm²

**Final Prediction**:
The best prediction for the area covered by the bacteria on Day 4 is **2.80 cm²**.

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