Question

In 1998 the enrollment at a community college was approximately 2500 students. In 2002 the enrollment had increased to 3250 students. If the enrollment continues to increase at this rate, what is a reasonable projection of enrollment for 2010?

Answer 1

Projected 2010 enrolment: `5492`

Explanation:

If the annual enrollment increases at a rate of `r`

Since the 1998 enrollment was 2500
and the 2002 enrollment was 3250
(and there are 4 years from 1998 to 2002)

`color(white)("XXX")2500xx(1+r)^4 =3250`

`color(white)("XXX")rarr (1+r)^4=3250/2500=13/10`

`color(white)("XXX")rarr (1+r)= root(4)(13/10)= 1.06779`

Since there are 8 years from 2002 until 2010:
projected enrollment in 2010 should (have been) `3250xx(1.06779)^8 ~~5492`