(a) What was the average annual change in enrollment from 1990 to 2003? ) Use the average annual change in enrollment to estimate the enrollments in 1994, 1998,

Question

The University of Florida had
enrollments of 36,531 students in 1990 and 48,673
students in 2003

b) Use the average annual change in enrollment to
estimate the enrollments in 1994, 1998, and 2002.

Answer 1

Humairaa:

 

The change in enrollment from 1990 to 2003 for (2003-1990=) 13 years is 48673-36531 = 12142. 

 

(a) The annual average change is 12142/13 = 934.

 

(b) Year 1994 is 4 years from 1990.  So the estimated change in enrollment is 4(934) = 3736.

     Year 1998 is 8 years from 1990.  So the estimated change in enrollment is 8(934) = 7472.

     Year 2002 is 12 years from 1990. So the estimated change in enrollment is 12(934) = 11208.

 

 

Dattaprabhakar (Dr. G.)

 

P.S. You have told me that the problem, being on linear equations, must be solved by "linear interpolation".  A more interesting problem is to estimate the enrollment using "compounding".  To explain, starting from 36531 in 1993, after the first year, the enrollment increases to 36531 (1 + r), in the second year it increases to [36351(1+r)](1+r) and so on.It reaches 48673 in 2003.  How to find r is interesting.

 

But that is probably beyond your scope, at least as of now.  If you would like to know, please post a comment.