Final answer:
The average annual change in enrollment from 1990 to 2003 is 934 students per year. The enrollments in 1994, 1998, and 2002 can be estimated using the average annual change. The equation of the line representing the data can be written, and its slope represents the average annual change in enrollment.
Step-by-step explanation:
To find the average annual change in enrollment from 1990 to 2003, we need to calculate the difference in enrollments between the two years and divide by the number of years.
(a) Average Annual Change = (Enrollment in 2003 - Enrollment in 1990) / (2003 - 1990)
Substituting the given data: Average Annual Change = (48,673 - 36,531) / (2003 - 1990)
Average Annual Change = 12,142 / 13
Average Annual Change = 934 students per year
(b) To estimate the enrollments in 1994, 1998, and 2002 using the average annual change, we can add or subtract the average annual change from the enrollments in 1990 and 2003.
Enrollment in 1994 = 36,531 + (4 * Average Annual Change)
Enrollment in 1998 = 36,531 + (8 * Average Annual Change)
Enrollment in 2002 = 36,531 + (12 * Average Annual Change)
(c) The equation of the line that represents the given data is Enrollment = Initial Enrollment + (Change in Enrollment / Number of Years) * Year
Slope of the line = Change in Enrollment / Number of Years
In this case, the slope is the average annual change in enrollment, which represents the rate at which the enrollment is increasing or decreasing each year.
(d) The concepts of slope and average rate of change in this context refer to the change in enrollment over a period of time. The slope provides a measure of the average change in enrollment per year, indicating the trend in the number of students. The average rate of change represents the change in enrollment per year on average.