To determine which type of function best models the data given in the table, we can analyze the growth values corresponding to the time values.
The data you've provided is:
- At 1 day: 0 inches
- At 3 days: 12 inches
- At 5 days: 32 inches
- At 7 days: 60 inches
Growth Differences
First, let's look at the differences in growth:
- From day 1 to day 3: 12 - 0 = 12 inches
- From day 3 to day 5: 32 - 12 = 20 inches
- From day 5 to day 7: 60 - 32 = 28 inches
These first differences (12, 20, 28) are not constant, suggesting that the growth is not linear.
Second Differences
Next, let's find the second differences:
- From 12 to 20: 20 - 12 = 8
- From 20 to 28: 28 - 20 = 8
The second differences are constant (8), indicating that the data can be modeled by a quadratic function.
Conclusion
From this analysis, the best conclusion is that the data is best modeled by a quadratic function.