Question

For 1983 through 1989, the per capita consumption of chicken in the u.S. Increased at a rate that was approximately linear. In 1983, the per capita consumption was 39.7 pounds, and in 1989 it was 47 pounds. Write a linear model for per capita consumption of chicken in the u.S. Let t represent time in years, where t = 3 represents 1983. Let y represent chicken consumption in pounds. What would you expect the per capita consumption of chicken to be in 1995? What would you expect the per capita consumption of chicken to be in 1995?

Answer 1

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:

$m=\frac{y_{2}-y_{1} }{t_{2}-t_{1}} =\frac{47-39.7}{9-3} =\frac{7.3}{6} =\frac{73}{60}$

We can write the required linear function as:

$y-39.7=\frac{73}{60}(t-3)$

Upon simplifying  this, we get:

$y=\frac{73}{60}t+\frac{721}{20}$

In order to find per capita consumption in 1995, we need to substitute t=15 in this function.

$y=\frac{73}{60}(15)+\frac{721}{20}=54.3$

Therefore, we would expect the per capita consumption of chicken in 1995 to be 54.3.