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 need to find the equation of the line that fits the given data points. We will use the two data points provided: (1940, 7) and (1997, 8).
First, we calculate the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
Applying the formula, we have:
slope = (8 - 7) / (1997 - 1940)
slope = 1 / 57
Next, we use the point-slope form of a linear equation with the coordinates (x1, y1) = (1940, 7) and the slope we just calculated:
(y - y1) = slope * (x - x1)
Substituting in the values:
(y - 7) = (1/57) * (x - 1940)
Now, let's find the estimated milk production in 1990 by substituting x = 1990 into the equation:
(y - 7) = (1/57) * (1990 - 1940)
(y - 7) = (1/57) * 50
57 * (y - 7) = 50
57y - 399 = 50
57y = 449
y ≈ 7.9
Therefore, the estimated milk production in 1990 is approximately 7.9 billion pounds.