Answer:
- A linear function best models the relationship.
Step-by-step explanation:
The question is incomplete. The table is missing.
The table is:
Time (years) Cost (thousands of dollars)
0 30
2 36.9
4 44.1
6 51.1
8 57.9
10 65.1
Solution
This problem is in the context of linear and exponential models. Then, you must choose whether a linear or exponential model best fit the data.
First, look at the input values, i.e. the time in years: they increase by constant difference of 2 years:
- 0 + 2 = 2,
- 2 + 2 = 4,
- 4 + 2 = 6,
- 6 + 2 = 8,
- 8 + 2 = 10.
Let's see if the data fit a linear model: calculate the difference between every consecutive outputs:
- 36.9 - 30 = 6.9 ≈ 7
- 44.1 - 36.9 = 7.2 ≈ 7
- 51.1- 44.1 = 7
- 57.9 - 51.1 = 6.8 ≈ 7
- 65.1 - 57.9 = 7.2 ≈ 7
Then, even though the difference is not exactly constant it is pretty close ot 7 (thousand dollars) every two years.
That is pretty good for models that try to predict data from the real world.
Then, you can safely assert that a linear function best models the relationship.
On the other hand, if you test for a constant ratio between consecutive outputs, which is what an exponential model returns, you would find:
- 44.1/36.9 = 1.195
- 51.1/44.1 = 1.159
Hence, this is far from a constant ratio and you can be sure this is not an exponential model.