We have been given that in 1983, the per capita consumption was 39.7 pounds, and in 1989 it was 47 pounds.
Let us assume t=0 corresponds to year 1980.
Hence, we can express the given information as ordered pairs as (3,39.7) and (9,47).
We can to find a linear function passing through these points. Let us first find slope of the linear function:
![m=\frac{y_{2}-y_{1} }{t_{2}-t_{1}} =\frac{47-39.7}{9-3} =\frac{7.3}{6} =\frac{73}{60}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bt_%7B2%7D-t_%7B1%7D%7D%20%3D%5Cfrac%7B47-39.7%7D%7B9-3%7D%20%3D%5Cfrac%7B7.3%7D%7B6%7D%20%3D%5Cfrac%7B73%7D%7B60%7D)
We can write the required linear function as:
![y-39.7=\frac{73}{60}(t-3)](https://tex.z-dn.net/?f=y-39.7%3D%5Cfrac%7B73%7D%7B60%7D%28t-3%29)
Upon simplifying this, we get:
![y=\frac{73}{60}t+\frac{721}{20}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B73%7D%7B60%7Dt%2B%5Cfrac%7B721%7D%7B20%7D)
In order to find per capita consumption in 1995, we need to substitute t=15 in this function.
![y=\frac{73}{60}(15)+\frac{721}{20}=54.3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B73%7D%7B60%7D%2815%29%2B%5Cfrac%7B721%7D%7B20%7D%3D54.3)
Therefore, we would expect the per capita consumption of chicken in 1995 to be 54.3.