1. Linear Functions: Application Example 1: The fall enrollment figures at a community college are shown. 2312 2465 2897 5 15 10 2000 2200 2400 2600 2800 3000 Number Of Years Past 1980 Enrollment

2. Linear Functions: Application a) Use the figures only for 1985 and 1995 to write a linear model (function) for the enrollment, y, in terms of the number of years past 1980, x. The point for 1985 is (5, 2312). The point for 1995 is (15, 2897). 2312 2465 2897 5 15 10 2000 2200 2400 2600 2800 3000 Number Of Years Past 1980 Enrollment

3. Linear Functions: Application (5, 2312) (15, 2897) First, use these points and the slope formula to find the slope of the line.

4. Linear Functions: Application Substitute one of the points and slope into the point-slope equation, y – y 1 = m(x – x 1 ), to get: y – 2312 = 58.5(x – 5). (5, 2312) (15, 2897)

5. Linear Functions: Application Next, put y – 2312 = 58.5(x – 5) in slope-intercept form. y – 2312 = 58.5x – 292.5 y = 58.5x + 2019.5

6. Linear Functions: Application b) Use the linear model to predict the enrollment in 2010. The year 2010 corresponds to x = 30 (30 years after 1980). Substitute this into the linear model to get: y = 58.5(30) + 2019.5 = 3774.5 According to the model, the enrollment in 2010 will be 3775 students.

7. Linear Functions: Application Try: The population of a small town for selected years is shown. 20896 22350 23104 3 9 6 20000 21000 22000 23000 24000 25000 Number Of Years Past 1990 Population

8. Linear Functions: Application Use the figures only for 1993 and 1999 to write a linear model (function) for the town's population, y, in terms of the number of years past 1990, x. Use the linear model to predict the town's population in 2010. y = 368x + 19792 According to the model, the town's population in 2010 will be 27,152.

9. Linear Functions: Application