Question

select the correct answer.
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. $(120 \cdot 3)^t = 3,240 ; t = 2$
c. $120(1.3)^t = 3,240 ; t = 27$
d. $120 + (3)^t = 3,240 ; t = 7$

Explanation:

Step1: Identify growth model

This is exponential growth, so the formula is $P(t) = P_0(r)^t$, where $P_0=120$, $r=3$, $P(t)=3240$. The equation is $120(3)^t = 3240$.

Step2: Isolate the exponential term

Divide both sides by 120:
$\frac{120(3)^t}{120} = \frac{3240}{120}$
$3^t = 27$

Step3: Solve for t

Rewrite 27 as $3^3$, so $3^t = 3^3$. Equate exponents: $t=3$.

Answer:

A. $120(3)^t = 3,240 ; t = 3$