A local college has increased its number of graduates by a factor of 1.045 over the previous year for every year since1999. In 1999, 924 students graduated. What explicit formula models this situation? Approximately how manystudents will graduate in 2014?

Answer:[tex]f(t) = 924 (1.045)^t[/tex]1788 students will graduate in 2014Step-by-step explanation:This is simple example of Geometric Progression.In 1999 the number of students are 924in 2000 the number of students will be 924 x (1.045)in 2001 the number of students will be 924 x (1.045)²in 2002 the number of students will be 924 x (1.045)³Hence the formula for this can be derived to be[tex]f(t) = 924 (1.045)^t[/tex]    where t is the total number of yearsSince 15 years passed from 1999 to 2014 we can use the formula to find the number of students that graduated[tex]f(15) = 924 (1.045)^1^5\\ f(15) = 1788.20[/tex]Since we cannot have a fraction of a student we round this down to 1788 students