Question

The United States Department of Agriculture tracks food availability in the country. In general, the amount of chicken available in the U.S. has been increasing steadily. In the year 2000, there were 54.2 pounds of chicken available per person, and in 2015, there were 62.6 pounds of chicken available per person. At the same time, the availability of red meat in the U.S. has been steadily decreasing. In 2000, there were 113.7 pounds of red meat available per person, and in 2015, there were 98.6 pounds of red meat available per person Assuming these trends continue, and assuming that a linear function can effectively model these trends, predict the year in which chicken availability surpasses red meat availability.

Answer 1

Based on the given data, we can use a linear function to predict the year when chicken availability surpasses red meat availability. By setting the two equations for chicken and red meat availability equal to each other and solving for the year, we can find that chicken availability will surpass red meat availability in the year 2030.

Step-by-step explanation:

To predict the year in which chicken availability surpasses red meat availability, we can use the linear function that models these trends. Let's define the year as 'x' and the chicken availability as 'y'. Based on the given data, the equation for chicken availability can be written as:

y = mx + b

where m represents the rate of increase in chicken availability per year and b represents the initial availability in the year 2000.

Using the values from the given data, we can find the slope (m) as:

m = (62.6 - 54.2) / (2015 - 2000)

Similarly, for red meat availability, the equation can be written as:

y = mx + b

Using the values from the given data, we can find the slope (m) as:

m = (98.6 - 113.7) / (2015 - 2000)

To find the year when chicken availability surpasses red meat availability, we need to find the value of 'x' for which 'y' (chicken availability) is greater than 'y' (red meat availability). By setting the two equations equal to each other and solving for 'x', we can find the year:

(62.6 - 54.2) / (2015 - 2000) * x + 54.2 = (98.6 - 113.7) / (2015 - 2000) * x + 113.7

Simplifying and solving for 'x', we get:

x = (54.2 - 113.7) / ((98.6 - 113.7) - (62.6 - 54.2))

x = 29.5

Therefore, the year in which chicken availability surpasses red meat availability is 2000 + 29.5 = 2029.5. Since 'x' represents a year, we can round up to the nearest whole year and predict that chicken availability will surpass red meat availability in the year 2030.