6 of 96 of 9 Items Question The table shows the amount of milk that Wisconsin dairy farms produced from 1940 to 1997. Use a linear model to estimate milk production in 1990. Year Milk Produced (in billions of lbs.) 1940 7 1972 7 1997 8 (1 point) Responses 15.1 15.1 12.5 12.5 7.5 7.5 2.5
To estimate milk production in 1990 using a linear model, we can use the given data points from the table to calculate the equation for a line that models the relationship between the years and milk production.
Let's start by finding the slope of the line using the formula:
slope = (change in milk production) / (change in year)
The change in milk production from 1940 to 1997 is 8 - 7 = 1 billion lbs.
The change in years from 1940 to 1997 is 1997 - 1940 = 57 years.
So, the slope is 1 / 57.
Next, we can use the slope-intercept form of a linear equation, y = mx + b, where y is the milk production, x is the year, m is the slope, and b is the y-intercept.
Now, let's calculate the y-intercept b using one of the given data points. We'll use the point (1940, 7).
7 = (1 / 57) * 1940 + b
Simplifying the equation:
7 = 0.017 * 1940 + b
7 = 32.98 + b
b = 7 - 32.98
b = -25.98
So, the equation for the linear model is:
y = (1 / 57) * x - 25.98
To estimate milk production in 1990 (x = 1990), we can plug the year into the equation:
y = (1 / 57) * 1990 - 25.98
y ≈ 34.56 - 25.98
y ≈ 8.58
Therefore, the estimated milk production in 1990 is approximately 8.58 billion lbs.