SOLUTION: 1. There were 2000 students enrolled in a school district in 1990. Over the next several year enrollments were seen to increase by roughly 8 percent per year. Assuming that the enr

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 1. There were 2000 students enrolled in a school district in 1990. Over the next several year enrollments were seen to increase by roughly 8 percent per year. Assuming that the enr      Log On


   

Question 536698: 1. There were 2000 students enrolled in a school district in 1990. Over the next several year enrollments were seen to increase by roughly 8 percent per year. Assuming that the enrollments continue to increase by 8 percent every year. Develop a difference equation model for the enrollment figures. Find the functional equation for your model and use it to predict the number of students in the school district for the year 2005.
Answer by fcabanski(1391) About Me  (Show Source):
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S(n+1)=S(n)+S(n)*.08=S(n)*(1.08)


The students in a year (S(n+1) means students in the current year) is equal to the number of students in the previous year plus .08 times the number of students in the previous year.


In the difference equation we have to know the number of students enrolled in a previous year. A functional equation tells us the students in a given year without knowing the number in the previous year.


S+=+2000%2A%281.08%29%5Et is the functional equation with S=# of students and t = number of years that have passed.


When 0 years have passed (1990) S=2000%2A%281.08%29%5E0=2000%2A1=2000


In 2005 15 years have passed so t=15.


S+=+2000%2A%281.08%29%5E15=6344.34=6344

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