Question

In 2005, there were 18,200 students at college A with a projected enrolment increase of 750 students per year in the same year there were 34.450 students at college with a procede decline of 500 students per year According to these projections when will the colleges have the same enrollment? What will be the enrolment in each college at that me? ment In the year , the enrollment at both colleges will be the same The total enrolment at each college will be students

Answer 1

a. 13 years

b. 27950 students

Explanation:

Let x be the number of years since the initial year 2005. In 2005,
`x = 0`, in 2006,
`x = 1`, and so on.

For college "A" the number of students is given by the function:

`NSA = 18200 + 750x`

For college "B" the number of students is given by the function:

`NSB = 34450 - 500x`

Matching these expressions you have the value of x for which the two colleges have the same number of students.

`NSA = 18200 + 750x = 34450 - 500x = NSB\\\\750x + 500x = 34450 - 18200\\\\1250x = 16250\\\\x = 16250/1250 = 13`

Then, the two colleges will have the same number of students 13 years later, that is, in 2018.

The number of students that each colleges will have in 2018 will be
`NSA = NSB = 18200 + 750 (13) = 27950` students.