Question

A local college has increased its number of graduates by a factor of 1.045 over the previous year for every year since

1999. In 1999, 924 students graduated. What explicit formula models this situation? Approximately how many
students will graduate in 2014?

Answer 1

`f(t) = 924 (1.045)^t`

1788 students will graduate in 2014

Explanation:

This is simple example of Geometric Progression.

In 1999 the number of students are 924

in 2000 the number of students will be 924 x (1.045)

in 2001 the number of students will be 924 x (1.045)²

in 2002 the number of students will be 924 x (1.045)³

Hence the formula for this can be derived to be

`f(t) = 924 (1.045)^t` where t is the total number of years

Since 15 years passed from 1999 to 2014 we can use the formula to find the number of students that graduated

`f(15) = 924 (1.045)^1^5\\ f(15) = 1788.20`

Since we cannot have a fraction of a student we round this down to

1788 students