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 33.7 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.

1. y = t + 27.05
2. y = 2.21667t
3. y = 27.05
4. y = 2.21667t − 27.05
5. y = 2.21667t + 27.05

Answer 1

D.
`y=2.2166x+27.05`

Explanation:

Considering time as dependent variable and The rate consumption as the dependent variable. And plotting them on x and y axes respectively taking our base year as 1980(at x=0)

We are given that

In Year 1983 i.e. x= 3

Rate of consumption = 33.7

Hence our coordinates are like (3,33.7)

In year 1989 i.e. x=9

Rate of consumption = 47

Hence our coordinates are like (9,47)

Hence considering it to be an linear relation, we have two points and now we use the two point form to evaluate the relation among them

Two point form is given as

`(y-y_1)/(x-x_1)=](y_2-y_1)/(x_2-x_1)`

`(x_1, y_1)= (3, 33.7)`

`(x_2, y_2)= (9, 47)`

Putting these values in formula

`(y-47)/(x-9)=(47-33.70)/(9-3)`

`(y-47)/(x-9)=(13.30)/(6)`

`(y-47)/(x-9)=2.2166`

`(y-47)=2.2166(x-9)`

`y=2.2166x - 2.2166*9+47`

`y=2.2166x - 2.2166*9+47`

`y=2.2166x+27.05`