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?

Question

Elijah Allen · Accepted Answer

Projected 2010 enrolment: #5492#

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#

Sophie Adams · Answer

undefined To find the reasonable projection of enrollment for 2010, we can use a linear interpolation method based on the given data points.

First, let's determine the change in enrollment from 1998 to 2002:

Change = 3250 students (2002) - 2500 students (1998) = 750 students

Next, let's calculate the annual increase in enrollment:

Annual increase = Change in enrollment / Number of years
                 = 750 students / 4 years
                 = 187.5 students/year

Now, let's project the enrollment for 2010:

Number of years from 2002 to 2010 = 2010 - 2002 = 8 years

Projected enrollment for 2010 = Enrollment in 2002 + (Annual increase × Number of years)
                              = 3250 students + (187.5 students/year × 8 years)
                              = 3250 students + 1500 students
                              = 4750 students

Therefore, a reasonable projection of enrollment for 2010 is approximately 4750 students.