Question

Which type of function best models the data in the table? Time and Growth Data Time (days) Growth (inches) 1 0 3 12 5 32 7 60 (1 point) Responses quadratic quadratic cubic cubic exponential exponential linear

Answer 1

To determine which type of function models the given data best, we can analyze the growth values in relation to the days:

- At day 1, the growth is 0 inches.
- At day 3, the growth is 12 inches.
- At day 5, the growth is 32 inches.
- At day 7, the growth is 60 inches.

Let's check the differences in growth:

1. **First Differences:**
- Between day 1 and day 3: 12 - 0 = 12
- Between day 3 and day 5: 32 - 12 = 20
- Between day 5 and day 7: 60 - 32 = 28

First differences: 12, 20, 28

2. **Second Differences:**
- Between 12 and 20: 20 - 12 = 8
- Between 20 and 28: 28 - 20 = 8

The second differences are constant (8), which suggests that the growth can be modeled by a **quadratic function**.

Given this analysis, the best model for the data provided is **quadratic**.