To find the initial weight of the kitten at 0 weeks given the table of values, we need to analyze the data provided and use the pattern observed in the weight gain over the weeks. Here’s the detailed step-by-step solution to determine the initial weight:
1. Identify the given data:
- Age in weeks: [tex]\(2, 4, 6, 8, 10\)[/tex]
- Corresponding weights in pounds: [tex]\(0.8, 1.4, 2.0, 2.6, 3.2\)[/tex]
2. Determine the pattern of weight gain:
- Calculate the difference in weight for each interval:
- [tex]\(1.4 - 0.8 = 0.6\)[/tex]
- [tex]\(2.0 - 1.4 = 0.6\)[/tex]
- [tex]\(2.6 - 2.0 = 0.6\)[/tex]
- [tex]\(3.2 - 2.6 = 0.6\)[/tex]
- The weight increases by [tex]\(0.6\)[/tex] pounds every 2 weeks.
3. Use the pattern to find the initial weight:
- From the data, at 2 weeks, the kitten weighs [tex]\(0.8\)[/tex] pounds.
- Since the weight is increasing linearly, we can determine the weight at 0 weeks by subtracting the difference for a 2-week interval from the weight at 2 weeks:
- Subtraction: [tex]\(0.8 - 0.6 = 0.2\)[/tex] pounds
4. Conclusion:
- The initial weight of the kitten at 0 weeks is [tex]\(0.2\)[/tex] pounds.
Thus, the correct answer is [tex]\(0.2\)[/tex] pounds.
