Whats the right answer
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
The correct answer is 7.5 billion lbs.
To estimate milk production in 1990 using a linear model, we can use the data points from the table to find the slope and y-intercept of the line.
First, we need to calculate the slope:
Slope = (Change in Milk Produced) / (Change in Year) = (8 - 7) / (1997 - 1940) = 1 / 57 ≈ 0.0175
Next, we can find the y-intercept using one of the data points. Let's use the data point from 1940: (1940, 7)
y-intercept = Milk Produced - (Slope * Year) = 7 - (0.0175 * 1940) ≈ 7 - 33.95 ≈ -26.95
Now we can use the linear equation:
Milk Produced in 1990 = (Slope * 1990) + y-intercept
= (0.0175 * 1990) + (-26.95)
≈ 34.825 - 26.95
≈ 7.875
Therefore, the estimated milk production in 1990 is approximately 7.875 billion lbs.
To estimate milk production in 1990 using a linear model, we can use the given data points from 1972 and 1997. The linear model assumes a constant rate of change between these two years.
First, we need to find the slope of the line, which represents the rate of change in milk production over time. The formula for calculating the slope (m) is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) represents the coordinates of the first data point (1972, 7) and (x2, y2) represents the coordinates of the second data point (1997, 8).
Using the given data points, we can calculate the slope:
m = (8 - 7) / (1997 - 1972) = 1 / 25
Next, we can use the slope-intercept form of a linear equation to find the y-intercept (b):
y = mx + b
Substituting the values of one of the data points (e.g., 1972, 7) and the slope (m) into the equation, we can solve for b:
7 = (1/25) * 1972 + b
7 = 78.88 + b
b = 7 - 78.88
b = -71.88
Now that we have the slope (m) and the y-intercept (b), we can plug in the x-value of 1990 into the equation to estimate milk production:
y = mx + b
y = (1/25) * 1990 + (-71.88)
y = 79.6 - 71.88
y = 7.72
Therefore, the estimated milk production in 1990 would be approximately 7.72 billion lbs.