Question

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 = 2
C.
120(1.3)t = 3,240; t = 27
D.
120 + (3)t = 3,240; t = 7

Answer 1

The answer is A

120(3)t = 3,240; t = 3  

Answer 2

Answer:

$120(3)^{t}$ = 3240 ; t=3

Step-by-step explanation:

Enrollment capacity for first year = 120

School plans to triple the capacity every year.

Let t be the number of years, Then capacity for every t year = $3^{t}$

Equation representing this situation is:

$120(3)^{t}$ = 3240

When we put t=3 in L.H.S,

$120(3)^{3}$ = 120×27

            = 3240

Hence, equation is satisfied when t=3.

That means, the school will achieve its target after 3 years.