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 1940 1972 1997
Milk Produced 7 7 8
• 15.1
• 12.5
• 7.5
• 2.5
Given that the linear model represents the trend in milk production, we can assume a constant rate of increase over time. To estimate milk production in 1990 using the linear model, we need to determine the slope and y-intercept of the line that best fits the data.
First, we need to calculate the slope. Using the formula for slope:
slope = (change in y) / (change in x)
slope = (8 - 7) / (1997 - 1940)
slope = 1 / 57
Next, we need to determine the y-intercept. We can use any of the data points to calculate it. Let's use the year 1940 data.
Using the slope-intercept formula:
y = mx + b
7 = (1/57)(1940) + b
7 = 33.96 + b
b = 7 - 33.96
b = -26.96
Now we can use the estimated slope and y-intercept to find the milk production in 1990.
Milk production in 1990 = (1/57)(1990) + (-26.96)
Milk production in 1990 ≈ 34.12 - 26.96
Milk production in 1990 ≈ 7.16
Therefore, the estimated milk production in Wisconsin in 1990 is approximately 7.16 units.