The table represents the cost of buying a piece of land in a remote village since the year 1990 which kind of function best models the realationship

A linear function best models the relationship.

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:

36.9/30 = 1.23 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.