To determine the type of growth based on the data provided for Tom's growth over time, we need to analyze the changes in growth values and see if they fit a specific pattern—linear, quadratic, cubic, or exponential.
The growth data is as follows:
- Day 1: Growth = 0
- Day 3: Growth = 12
- Day 5: Growth = 32
- Day 7: Growth = 60
Let's find the differences in growth:
- From Day 1 to Day 3: \(12 - 0 = 12\)
- From Day 3 to Day 5: \(32 - 12 = 20\)
- From Day 5 to Day 7: \(60 - 32 = 28\)
Now, we calculate the second differences (the differences of the differences):
- From 12 to 20: \(20 - 12 = 8\)
- From 20 to 28: \(28 - 20 = 8\)
The second differences are constant (both are 8), which implies that the growth data is a quadratic function.
In summary, the growth data shows quadratic growth, as indicated by the constant second differences.