Question

For the period 1983 through 1989, where per capita chicken consumption in the U.S. increased linearly, write a linear model for per capita chicken consumption in pounds (y) over time (t), where t = 3 represents 1983.

a. y = 2.3t − 25.3
b. y = 2.3t + 25.3
c. y = 2.3t
d. y = t + 25.3
e. y = 25.3

Answer 1

The correct linear model for per capita chicken consumption in the U.S. for 1983 through 1989, where t = 3 represents 1983, is y = 2.3t + 25.3.

Correxct option is b. y = 2.3t + 25.3

Step-by-step explanation:

The question asks to write a linear model for per capita chicken consumption in the U.S. for the period of 1983 to 1989, with 't' representing the year where t = 3 corresponds to 1983. A linear model is represented in the form of y = mt + b, where 'm' is the slope and 'b' is the y-intercept. Because the model must pass through the point where t = 3 (year 1983), we can analyze the options provided to see which one makes sense based on the context and the given parameters.

Option (a) suggests a decrease when t = 3, which doesn't align with the positive trend indicated by the rise in chicken consumption. Option (b) is the best fit because when t = 3, the model gives a positive value, corresponding to the increase in consumption. The linear equation y = 2.3t + 25.3 increases over time and gives a positive value for chicken consumption in 1983, in line with the data provided by the U.S. Department of Agriculture (USDA), which showed an overall increase in chicken consumption over time.