A graduate school plans to increase its enrollment capacity by developing its facilities and the programs it offers. Their enrollment capacity this year was 120 graduate students. Beginning next year, the school plans to triple this number every year, with a target enrollment capacity of 3,240 students. Which equation represents this situation, and after how many years, t, will the graduate school be able to achieve its target enrollment capacity? A. 120(3)t = 3,240; t = 3 B. 120 + (3)t = 3,240; t = 7 C. (120 · 3)t = 3,240; t = 2 D. 120(1.3)t = 3,240; t = 27

Accepted Solution

Answer:A. 120(3)t = 3,240; t = 3Step-by-step explanation:We are given that enrollment capacity for first year = 120The school plans to triple the capacity every year.Assuming t to be the number of years, the capacity for every t year will be [tex]3^t[/tex]. This is expressed by the equation [tex]120(3)^t = 3240[/tex]Substituting t =3 in the above equation to get:[tex]120(3)^3 = 120\times 27=[/tex] 3240So the equation is true when t = 3.Therefore, the correct answer option is A. 120(3)t = 3,240; t = 3.