To determine which type of function best models the growth data, we can look at the provided time and growth values:
- At time 1 day, the growth is 0 inches.
- At time 3 days, the growth is 12 inches.
- At time 5 days, the growth is 32 inches.
- At time 7 days, the growth is 60 inches.
From the values, we can notice the growth is initially slow, then increases at a faster rate as time progresses. This pattern suggests that the growth is not linear, since a linear function would show a consistent rate of growth.
To consider if the growth is quadratic or exponential, let's examine the differences in growth:
- Growth from 0 to 12 inches (from day 1 to day 3) is 12 inches.
- Growth from 12 to 32 inches (from day 3 to day 5) is 20 inches.
- Growth from 32 to 60 inches (from day 5 to day 7) is 28 inches.
The increase in growth amounts is not consistent, implying that a linear model isn't suitable. However, we can see that the rate of increase itself is increasing (12 to 20 to 28), which suggests that it may be fitting a quadratic function rather than an exponential function.
Based on this analysis, the best model for the given data would be:
quadratic.