Teaneck High had an enrollment of 11040 in 1985 and an enrollment of 12100 in year 1998. What is the predicted enrollment of Teaneck High in 2014 if we assume a linear model?
To predict the enrollment of Teaneck High in 2014 using a linear model, we need to find the equation of the line that best fits the given data points.
We have two data points: (1985, 11040) and (1998, 12100). We can use these points to form the equation of the line in the form y = mx + b, where y represents the enrollment and x represents the year.
First, we need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values (1985, 11040) for (x1, y1) and (1998, 12100) for (x2, y2), we get:
m = (12100 - 11040) / (1998 - 1985)
m = 1060 / 13
m = 81.54 (rounded to two decimal places)
Next, we need to determine the y-intercept (b) of the line. We can use the slope-intercept form of the equation (y = mx + b) and substitute one of the given data points. Let's use (1985, 11040):
11040 = 81.54(1985) + b
11040 = 161870.9 + b
Now, we solve for b:
b = 11040 - 161870.9
b ≈ -150830.9 (rounded to two decimal places)
So, the equation of the line is:
y = 81.54x - 150830.9
To predict the enrollment in 2014 (x = 2014), we substitute this value into the equation:
y = 81.54(2014) - 150830.9
y ≈ 10799 (rounded to the nearest whole number)
Therefore, the predicted enrollment of Teaneck High in 2014, assuming a linear model, is approximately 10,799 students.
To predict the enrollment of Teaneck High in 2014 using a linear model, we can use the formula for a linear equation:
y = mx + b
Where:
y = predicted enrollment
x = year
m = slope of the line (change in enrollment per year)
b = y-intercept (enrollment in the base year)
First, we need to calculate the slope (m) using the given information:
Change in enrollment = (enrollment in 1998 - enrollment in 1985)
= (12100 - 11040)
= 1060
Change in year = (1998 - 1985)
= 13
Slope (m) = Change in enrollment / Change in year
= 1060 / 13
≈ 81.54
Next, we need to find the y-intercept (b). We can use the base year of 1985:
b = y - mx
b = 11040 - (81.54 * 1985)
b ≈ -146,713.9
Now, we have the slope (m) and the y-intercept (b). We can substitute these values into the linear equation to find the predicted enrollment in 2014 (x = 2014):
predicted enrollment (y) = mx + b
predicted enrollment (y) = 81.54 * 2014 - 146713.9
predicted enrollment (y) ≈ 12,910.76
Therefore, the predicted enrollment of Teaneck High in 2014 using a linear model is approximately 12,910 students.
Assuming linear variation, rate of increase,
r = (12100-11040)/(1998-1985)
Predicted enrollment in 2014,
E(2014) = E(1998)+(2014-1998)r
= 12100 - (2014-1998)r
Calculate for E(2014).